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Solve various math problems ranging from unit conversions to cost calculations in transportation and shopping scenarios. Explore solutions for problems involving metric and traditional units of measure, money printing, tree-saving initiatives, and more.
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PROBLEM OF THE DAY SCHOOL DAY 91-180
School Day 91 The numbers on the left of the equal signs are correct, but some decimal points and/or zeros are incorrect in the numbers to the right of the equal signs. Correct the decimal points and/or zeros to make each statement true. Do you find it easier to convert between metric units of measure (i.e. mL to L) or between traditional units of measure (i.e. cups to quarts). Explain why. (a) 0.13 mL = 0.0013L (b) 6 mL = 600 L (c) 23 L = 0.00023 mL
Solution for Day 91 (a) 0.13 mL = 0.0013 L (b) 6 mL = 0.006 L (c) 23 L = 23000 mL
School Day 92 A 10-gallon hat is the name for the large hat that many cowboys of the Old West wore. Although this hat was big, it only held about ¾ of a gallon. How many quarts did the 10-gallon hat actually hold? How many liters? How many milliliters? (1 gallon ≈ 3.8 liters)
Solution for Day 92 How many quarts did the 10-gallon hat actually hold? 3 Quarts How many liters? 3.8 x ¾ = 2.85 L How many milliliters? 2850 mL
School Day 93 A bottle of medicine contains 4 fluid ounces. One dose of medicine is 3 teaspoons. How many doses of medicine are in the bottle? If you reduce the dose to 2 teaspoons, how many doses will you get? If you increase it to 4 teaspoons, how many doses are possible? FYI: 3 teaspoons = 1 Tablespoon 2 Tablespoons = 1 fluid ounce 8 fluid ounces = 1 cup
Solution for Day 93 How many doses of medicine are in the bottle? 24 tsp = 4 fl oz 8 doses at 3 tsp. each If you reduce the dose to 2 teaspoons, how many doses will you get? 12 doses at 2 tsp each If you increase it to 4 teaspoons, how many doses are possible? 6 doses at 4 tsp each
School Day 94 There are 0.3048 meters in a foot. How many meters long is a 12-foot cable? What percentage of a meter is a foot? What percentage is a foot of a meter? What percentage of a yard is a meter? What percentage of a meter is a yard? Explain why your answers make sense.
Solution to Day 94 How many meters long is a 12-foot cable? What percentage of a meter is a foot? What percentage is a foot of a meter? What percentage of a yard is a meter? What percentage of a meter is a yard? 109.36% Explain why your answers make sense. 3.6576 m 30.48% 328.08% 91.44%
School Day 95 Taxi fares depend upon the distance that is traveled and the number of passengers. Tony’s Taxi charges $3 for the first mile and $1 for each additional half mile (or fraction thereof). If the taxi ride is 5¼ miles, what is the fare? What if you had $15, how many miles could you travel? When traveling, transportation costs can add up, what are some costs associated with vacationing?
Solution to Day 95 If the taxi ride is 5¼ miles, what is the fare? $12.00 What if you had $15, how many miles could you travel? 6 miles
School Day 96 An odometer records the number of miles a car has traveled. When the Santos family left for Florida, the odometer read 8765.2 miles. When they arrived in Florida, it was 9382.7 miles. They drove 18.6 miles while they were in Florida. They returned home of the same roads they used for driving to Florida. If gasoline is $3.50/gal and their car gets 22 mpg, how much did it cost them for their trip? How could they have reduced their transportation costs?
Solution for Day 96 If gasoline is $3.50/gal and their car gets 22 mpg, how much did it cost them for their trip? 1253.6 miles and about 57 gallons $199.50 How could they have reduced their transportation costs?
School Day 97 A stack of recyclable newspaper 36 inches high will save one tree. If you save a stack of newspapers 14 feet high, about how many trees are saved? If you wanted to save 100 trees, how many feet high would the stack have to be? What is the ratio between the height of the newspaper stack in feet and the number of trees saved?
Solution to Day 97 If you wanted to save 100 trees, how many feet high would the stack have to be? 280 ft high stack for 100 trees What is the ratio between the height of the newspaper stack in feet and the number of trees saved? 3ft : 1 tree
School Day 98 A printing press that prints money can print 8,000 sheets of 32 bills every hour. If five-dollar bills are printed, what is the value of the money printed during an 8-hour shift? What is the ratio of sheets per minute?
Solution for Day 98 If five-dollar bills are printed, what is the value of the money printed during an 8-hour shift? $10,240,000 What is the ratio of sheets per minute? 133 1/3 sheets : 1 minute
School Day 99 At a Dollar-Day Sale everything in the designated section of the store is priced at a dollar or in multiples of a dollar. Mary and Joe went shopping during this sale. The cost of the items they decided to buy was $25. They must pay sales tax at 6¢ per dollar or 6%. What is the total cost of their purchase? If $10 of the $25 was clothing, how does that change the PA sales tax charge? What is their total purchase with this change?
Solution for Day 99 What is the total cost of their purchase? $26.50 If $10 of the $25 was clothing, how does that change the PA sales tax charge? $0.90 tax instead of $1.50 What is their total purchase with this change? $25.90
School Day 100 A successive discount is a discount after a previous discount has been made. Successive discounts can lead to big savings. The price of a jacket is reduced 40%. For one Day only the reduced price is reduced another 10%. Is this the same as a 50% discount? Use an example to support your answer.
Solution for Day 100 Is this the same as a 50% discount? Use an example to support your answer. No, it is not the same. Example: $100 original price 40% off leaves a $60.00 cost Additional 10% of 60.00 is $6.00 Total Discount is $46.00 with a $54.00 cost 50% off leaves a $50.00 cost
School Day 101 Buying things on sale is a great way to save money. A CD is marked 30% off the original price. The sale price is $12.60. Ignoring the sales tax, find the original price of the CD. Explain why you think it is more cost effective to purchase CD’s or download specific songs.
Solution to Day 101 Ignoring the sales tax, find the original price of the CD. X (70%) = 12.60 $18.00 Explain why you think it is more cost effective to purchase CD’s or download specific songs.
School Day 102 A “tip” is a gratuity, or a payment for good service. In most cases a tip of 15%, before sales tax is added, is acceptable. Three people went to lunch together. The bill came to $23.91, plus 6% sales tax. They decided to leave a 15% tip and divide the cost of lunch equally, each paying the same amount. How much would each person pay for lunch with tip and tax? Round to the nearest cent. In the high-end city restaurants, the expected tip can be higher, even up to 25%. What is your opinion about tipping for service?
Solution for Day 102 How much would each person pay for lunch with tip and tax? Round to the nearest cent. $9.65 pp In the high-end city restaurants, the expected tip can be higher, even up to 25%. What is your opinion about tipping for service?
School Day 103 If an investment increases at about the same rate each year, the Rule of 72 may be used to estimate how many years it will take for the original amount of money to double. For example, if $1,000 is invested at an interest rate of 6%, divide 72 by 6 (6% x 100 = 6). Since the quotient is 12, it would take 12 years for the $1,000 to double. Try it with $6,000 and 10.5% - about how many years would it take to double? How does this knowledge affect how you save money for things you want?
Solution for Day 103 Try it with $6,000 and 10.5% - about how many years would it take to double? About 7 years 72 /10.5 = 6.85 How does this knowledge affect how you save money for things you want?
School Day 104 Memorabilia are the kinds of things that everybody once had, but few can find years later. Because they are hard to find, such items may become worth much more money than they originally cost, TV Guide, for example. Assuming an issue of TV Guide that once sold for $0.15 now sells for $7, what is the percent of increase? What commonplace items of today do you think will become collectable in 20 years?
Solution for Day 104 Assuming an issue of TV Guide that once sold for $0.15 now sells for $7, what is the percent of increase? 7.00 – 0.15 = 6.85 6.85 / 0.15 x 100 = 4566 2/3 % or 4566.666 of increase What commonplace items of today do you think will become collectable in 20 years?
School Day 105 Henry Ford worked to produce an inexpensive, universal car. When introduced in 1908, his Model T retailed for $850, but by 1924 – because of mass production - it was selling for $250. Find the percent of decrease and round your answer to the nearest percent. The average net income in 1928 was $6,078.93 per year. If you could save $5 a week to buy a $250 car, how long would it take you? How much would you have to save each week to buy a new economy car today?
Solution for Day 105 Find the percent of decrease and round your answer to the nearest percent. 850-250 = 600 600/850 x 100 = 70.59% rounded to 71% of decrease The average net income in 1928 was $6,078.93 per year. If you could save $5 a week to buy a $250 car, how long would it take you? How much would you have to save each week to buy a new economy car today? 6078.93 / 5 = 50 weeks of saving
School Day 106 Prepackaging is common in supermarkets. A prepackaged item has been cut, weighed, and priced to make shopping more convenient for customers. According to the label on the package of turkey, the turkey weighs 14.56 pounds. It is priced $0.79 per pound. Find the cost of the turkey and round your answer up to the penny. If you buy in bulk, you get a lower price per pound. If you buy 20 pounds the cost is $0.60 per pound, how much more will it cost you? Is it cost effective to purchase in bulk?
Solution to Day 106 Find the cost of the turkey and round your answer up to the penny. $11.51 If you buy in bulk, you get a lower price per pound. If you buy 20 pounds the cost is $0.60 per pound, how much more will it cost you? 20 x 0.60 = 12.00 12.00 – 11 51 = $0.49 extra cost Is it cost effective to purchase in bulk?
School Day 107 Environmentalists estimate that during a lifetime, an average person will throw away garbage that is equivalent to 600 times his or her adult weight. Using this information, about how much would an adult who threw away 54 tons of trash weigh? What kinds of waste products are produced in your industry? What is the cost of their removal or recycling?
Solution for Day 107 Using this information, about how much would an adult who threw away 54 tons of trash weigh? 1 ton = 2000 lbs (54 x 2000)/600 = 180 lbs What kinds of waste products are produced in your industry? What is the cost of their removal or recycling?
School Day 108 Bamboo, a tall, treelike grass found in tropical or semitropical regions, may grow as much as 1.5 feet per Day. It may reach a maximum height of 120 feet. If bamboo grows at its fastest rate, how long would it take to reach its maximum height? Using bamboo is considered environmentally positive. Do you agree with this and why?
Solution to Day 108 If bamboo grows at its fastest rate, how long would it take to reach its maximum height? 120 / 15 = 80 Days Using bamboo is considered environmentally positive. Do you agree with this and why?
School Day 109 Kathy plans to cook a turkey dinner for her family. The turkey, which weighs about 16 pounds, takes about 6 hours to cook. Before serving, however; it must set 30 minutes. About what time should Kathy start to cook the turkey if she wants dinner to begin at 7 PM? Why is timing important in preparing food?
Solution to Day 109 About what time should Kathy start to cook the turkey if she wants dinner to begin at 7 PM? 12:30 PM Why is timing important in preparing food?
School Day 110 Math Textbook vs. Real World. Suppose Sam runs a lap around the high school track in 2.5 minutes. How long will it take him to run 6.5 laps - the math textbook answer would be 16.25 minutes. In real life this answer is possible, but unlikely. What would you estimate as a realistic time for the 6.5 laps? Why is there a difference between the math textbook and real life?
Solution to Day 110 What would you estimate as a realistic time for the 6.5 laps? Variable answer and questions! Why is there a difference between the math textbook and real life?
School Day 111 An average adult’s heart beats 80 times per minute. An average canary’s heart beats 130 times in 12 seconds. Of the two heartbeats above, which is faster, and about how many times as fast is it? Does your answer make sense? Explain why or why not.
Solution to Day 111 Of the two heartbeats above, which is faster, and about how many times as fast is it? Set up a proportion and solve for the missing value 130 times : 12 seconds = X : 60 seconds Canary is 650 bpm which is 8 times faster Does your answer make sense? Explain why or why not.
School Day 112 The escape velocity is the minimum velocity (speed) that an object needs to overcome the pull of gravity from another object. For a spacecraft to leave Earth, it would need to achieve an escape velocity of about 7 miles per second. This is faster than the speed of sound, which travels at about 760 miles per hour (at 0°C). Express the Earth’s escape velocity in miles per hour. About how many times the speed of sound is this? Explain how you solved this problem.
Solution for Day 112 Express the Earth’s escape velocity in miles per hour. 25,000 mph About how many times the speed of sound is this? 33 times the speed of sound Explain how you solved this problem.
School Day 113 A light year is the distance a ray of light travels in one year (about 186,000 miles per second). After the sun, the nearest star to the Earth is Proxima Centauri at about 4.3 light years away. A parsec is another way to measure great distances in space. Proxima Centauri is about 1.3 parsecs from Earth. About how many parsecs equal a light year? About how many light years equal a parsec? Do your answers make sense?
Solution to Day 113 About how many parsecs equal a light year? About 3.2 light years About how many light years equal a parsec? About 0.3 parsecs Do your answers make sense?
School Day 114 Each quarter, Mary’s teacher gives four tests. No test has any extra credit or bonus problems. So far, Mary’s test grades are two 85s and 89. The last test of the quarter is scheduled for next week. Can Mary obtain an “A” test average for the quarter? Explain.
Solution for Day 114 Can Mary obtain an “A” test average for the quarter? Mary would need a 101 on her last test. Explain.
School Day 115 A batting average is the number of hits a batter makes, divided by the official number of at-bats he or she has had. Bases on balls and sacrifices do not count as official times at-bat. A player’s batting average is expressed by a 3-digit decimal, rounded to the nearest thousandth. What is the batting average of a player who has been to the plate 45 times, and of these times to the plate has 10 hits, 7 bases on balls and 3 sacrifices?
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