1 / 12

Translating English into Algebra

Translating English into Algebra.

summer
Download Presentation

Translating English into Algebra

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Translating English into Algebra There is much confusion and scratching of heads and gnashing of teeth on topics where you have English sentences that have to be converted into math. The secret is twofold. First, practice and secondly more practice. Method of Working that I do every time:I read the question and eventually it tells me what they want me to find, knowing the key phrases that can be translated into Algebra.

  2. Example 1 • The age of one brother combined with twice the age of a second brother is 50. The difference between twice the age of the first brother and the age of the second brother is 10 years. SOLUTION:OK, first a definition:--> Let x = age of first brother--> Ley y = age of second brother. In questions like this, we generally have 2 unknowns. If that is true, then we need enough information to generate 2 equations from which to solve both unknowns. Again, we usually have 2 sentences, each one will produce one of the required equations.

  3. Break down the sentences • Looking at the sentence:"The age of one brother combined with twice the age of a second brother is 50" we need to convert this to algebra, so "The age of one brother" "combined with" "twice the age of a second brother" "is" "50“ ________x__________ + ___________2y___________ __=__ _50_ if you EVER get stuck converting something like "twice the age of a second brother", then just pick examples, egIF he was 10, then twice his age would be (10+10 OR 2*10) --> 20so, IF he was y, then twice his age would be (y+y OR 2*y) --> 2y --> x+2y = 50

  4. Looking at the next sentence:"The difference between twice the age of the first brother and the age of the second brother is 10 years", so "The difference between twice the age of the first brother and the age of the second brother is 10"___subtract them 2x ___________y_________ = _10_ again, if confused, pick 2 easy numbers to test your translation: eg the difference betwee 10 and 6 is? well the answer is 4, gotten from 10-6 --> 2x-y = 10 So we have 2 equations now, which need solving: we can save this for later

  5. Example 2 The older brother Bob is two year older than his little sister Alice. Taken together, the sum of their ages is 8. • 1. Read the problem carefully. • 2. Get rid of clutter • 3. Identify key variables (unknowns). • 4. Eliminate unneeded variables. • 5. Use the text of the problem to write equations. • 6. Solve the equation. • 7. Find the remaining variables.

  6. The older brother Bob is two year older than his little sister Alice. Taken together, the sum of their ages is 8. Bob is two years older than Alice. Bob's age plus Alice's age = 8. Bob's age B and Alice's age A Get rid of B. Bob is 2 years older than Alice, so you can use A+2 instead of B Sum of their ages is 8. A + (A+2) = 8. Solve the equation

  7. Solution to Example 2 Solving, you just found Alice's Age A=3. Bob's age is two years older, which is 5.

  8. Example 3 • Problem:   Jeanne has $17 in her piggy bank. How much money does she need to buy a game that costs $68?

  9. Solution to Example 3 Solution:   Let x represent the amount of money Jeanne needs. Then the following equation can represent this problem:   17 + x = 68

  10. Solution to Example 3 • We can subtract 17 from both sides of the equation to find the value of x. 68 - 17 = x • Answer:   x = 51, so Jeanne needs $51 to buy the game

  11. Practice • If 4 is subtracted from twice a number, the result is 10 less than the number. Find the number. What is your answer? 2. Karin’s mom runs a dairy farm. Last year Betty the cow gave 375 gallons less than twice the amount from Bessie the cow. Together, Betty and Bessie produced 1464 gallons of milk. How many gallons did each cow give? What is your answer?  3. Twice a number is added to the number and the answer is 90. Find the number. What is your answer?

  12. More Practice  4. Jose has a board that is 44 inches long. He wishes to cut it into two pieces so that one piece will be 6 inches longer than the other. How long should the shorter piece be? What is your answer? 5.  Paula received a paycheck of $585. This amount reflects her weekly earnings less 10% of her earnings for deductions. How much was she paid before deductions were taken out? What is your answer? 6.  The perimeter of a triangular lot is 72 meters. One side is 16 meters, and the other side is twice the first side. Find the length of the third side.

More Related