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Money Problems:. By Dr. Marcia Tharp and Dr. Julia Arnold. In money problems we encounter two types of numbers: For example, if we say “the number of coins is 6”, 6 represents how many coins. If we say the value of the coins is 60 cents, then 60 represents how much the coins are worth.
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Money Problems: By Dr. Marcia Tharp and Dr. Julia Arnold
In money problems we encounter two types of numbers: For example, if we say “the number of coins is 6”, 6 represents how many coins. If we say the value of the coins is 60 cents, then 60 represents how much the coins are worth. The two ideas are: how many and value of See if you can pick out the the number for how many, and the number for the value of in the next problem.
Example 1 The Hurrah Players sold 600 tickets to a recent event. Adults paid $5 each and students paid $2 each. If the total collected was $2025, how many tickets of each type were sold? 600 is how many $5, $2, and $2025 represents the value of
If you have 5 nickels, what is the value of the money? 25 cents If you have $3.00 in dimes, how many dimes do you have? 30 How did you get the numbers above? In the nickel problem you multiplied the “number of” by the “value of” and thus 5 * .05 = .25 = 25 cents In the dime problem you divided the value of the money by the value of one dime dimes
The Hurrah Players sold 600 tickets to a recent event. Adults paid $5 each and students paid $2 each. If the total collected was $2025, how many tickets of each type were sold? R Read the problem over and over until you feel you understand the problem. You might make a casual guess. 250 adult and 350 student tickets for example 1. How could you check your guess? By multiplying the “how many” number by the “value of” number. 250 * $5 + 350 * $2 = $1950 Since the total is not $2025 we know this guess isn’t right.
I’m ready to get this problem done so algebra is going to be a lot quicker than guessing. Let’s chart the information as follows: This is the information I have! How many Value of Total Tickets 5 Adult Student 2 Total 600 2025
How many Value of Total Tickets x 5 Adult Student 2 Total 600 2025 Now let’s add the algebra. Since the number of adult tickets is unknown, let # of adult tickets = x How would we represent the number of student tickets? If you said x, that would make x = 300 automatically since x also represents adult tickets. Not right.
How many Value of Total Tickets x 5 Adult Student 2 Total 600 2025 How would we represent the number of student tickets? When you know a total (600) and x represents part of that total, use subtraction total - part 600-x = number of student tickets. 600 - x
How many Value of Total Tickets x 5 Adult Student 2 Total 600 2025 Now we must multiply “how many” by “value of” and put in total column. 5x 2(600 - x) 600 - x
Form the equation. The money from the student tickets and the money from the adult tickets should add up to equal the total amount collected. cost adult tickets + cost student tickets = total collected 5x + 2(600 – x) = 2025 5x + 1200 - 2x = 2025 3x + 1200 = 2025 3x = 825 x = 275 adult tickets 600 - 275 = 325 student tickets
Directions: work out problems 1-6 then check the solutions found on next slide. 1. Yolanda has dimes and quarters totaling $5.25. If she has 33 coins in all how many of each does she have? 2. Tony has 39 bills in fives and tens. If the total value is $285 how many of each does he have? 3. The Drama Club sold 500 tickets to their fall performance. The adult tickets were $5 each and the student tickets were $3 each. If they took in $2080, how many of each did they sell? 4. Edie has 27 coins in dimes and quarters. If the total value is $3.75 how many of each does she have?
5. Venus bought 40 stamps for $12.40. Some of the stamps were 33-cent stamps and some were 23 cent stamps. How many of each did she buy? 6. Sonia has 26 bills in ones and fives. If their total value is $50 how many of each does she have?
Answers to Practice Problems • 20 dimes and 13 quarters • 21 fives and 18 tens • 290 adult tickets and 210 student tickets • 20 dimes and 7 quarters • 32 stamps at 33cents each and 8 stamps at 23 cents each • 20 $1 bills and 6 $5 bills Complete Solutions Follow
1. Yolanda has dimes and quarters totaling $5.25. If she has 33 coins in all how many of each does she have? .10x + .25(33-x)= 5.25 .10x +8.25 - .25x=5.25 -.15x=-3 x = 20 dimes 33-x = 13 quarters Total 33 coins $5.25 The equation is the sum of the last column =‘s total or .10x + .25(33-x)= 5.25
2. Tony has 39 bills in fives and tens. If the total value is $285 how many of each does he have? 5x + 10(39 – x)= 285 5x + 390 –10x =285 -5x = -105 x = 21 fives 39-x = 18 tens Total 39 bills $285 The equation is the sum of the last column =‘s total or 5x + 10(39 – x)= 285
3. The Drama Club sold 500 tickets to their fall performance. The adult tickets were $5 each and the student tickets were $3 each. If they took in $2080, how many of each did they sell? 5x + 3(500 – x)= 2080 5x + 1500 –3x =2080 2x = 580 x = 290 adult tickets 500-x = 210 student tickets Total 500 tickets $2080 The equation is the sum of the last column =‘s total or 5x + 3(500 – x)= 2080
4. Edie has 27 coins in dimes and quarters. If the total value is $3.75 how many of each does she have? .10x +.25(27 – x) = 3.75 .10x +6.75 - .25x =3.75 -.15x = -3 x = 20 dimes 27-x = 7 quarters Total 27 coins $3.75 The equation is the sum of the last column =‘s total or .10x +.25(27 – x) = 3.75
5. Venus bought 40 stamps for $12.40. Some of the stamps were 33-cent stamps and some were 23 cent stamps. How many of each did she buy? .33x + .23(40-x)=12.40 .33x +9.2 -.23x=12.40 .10x = 3.20 x = 32 33 cent stamps 40-x = 8 23 cent stamps Total 40 stamps $12.40 The equation is the sum of the last column =‘s total or .33x + .23(40-x)=12.40
6. Sonia has 26 bills in ones and fives. If their total value is $50 how many of each does she have? x + 5(26 – x)=50 X + 130 –5x = 50 -4x = -80 X = 20 ones 26 – x = 6 fives Total 26 bills $50 The equation is the sum of the last column =‘s total or x + 5(26 – x)=50
