Solving Verbal Equations

1. Solving Verbal Equations

2. Warm-up • Translate the following into mathematical expressions • One number multiplied by the sum of two different numbers • The product of three different numbers decreased by a fourth number • A number subtracted from the product of two different numbers • The difference between two numbers multplied by a third number.

3. Warm-up Continued • Translate the following into mathematical expressions • The sum of a number and seven divided by a different number • The product of fourteen and a number, decreased by another number • Seven less than a number is nineteen. • A number increased by twelve is the same as ten added to twice that number.

4. Product of Is the same as Quotient Decreased by More than is Increased by Divided by Added to Less The quantity of The difference Verbal Equations What operation does the phrase tell me to do?

5. How to solve Verbal Equations • Step 1: Write the algebraic expression • Step 2: Solve for the variable • Step 3: Check your answer

6. Example 1 • Fifteen is added to two times a number and the result is fifty-five. Write the algebraic equation Solve for the variable Check your answer.

7. Example 2 • Two consecutive integers sum up to 303. Find the integers. What do I use to represent consecutive integers again? Am I done?

8. Example 3 • If three times a number is decreased by thirty, the result is equal to two times the number. Find the number. Am I done?

9. Example 4 • The last math test that you took had 100 regular points and 10 bonus points. You received a total score of 87, which included 9 bonus points. What would your score have been without any bonus points? First Step: Write a model in words indicating what you have. Step 2: Fill in what you know Step 4: Check your answer Regular points Step 3: Solve for your variable Bonus points Total score Are you done?

10. Example 5 • The perimeter of a rectangular shaped lot is 420 meters. The length is twice the width. Find both dimensions. • Step 1: draw a picture 2x x 2x + x + 2x + x = 420 x = 70 Am I done? width = 70, length = 140

11. Example 6 • Four people are sharing the cost of a monthly phone bill of $58.25, what is each person’s share of the bill? Does this cover the whole bill?

12. Example 7 The balance in your bank account is $642.35. If you use your check card to buy some Halloween decorations, your balance would be $476.79. How much do the decorations cost?

13. Consecutive Integers • How do you represent consecutive integers? Let’s try representing three consecutive integers • Why do I add by 1 each time? x x+1 x+2

14. Consecutive Even Integers • How do you represent consecutive even integers? Let’s try three of them again. • Why do I multiply the first by 2? • Why do I add by 2 each time? 2x 2x+2 2x+4

15. Consecutive Odd Integers • How do you represent consecutive odd integers? Hey let’s try three yet again. • Why did I multiply by 2 and add 1 the first time • Why do I add by 2 each time? 2x+1 2x+3 2x+5

16. Example 8 • Find two consecutive integers that sum up to fifty-three. The two integers are 26 and 27

17. Example 9 • Find three consecutive integers such that the sum of the first and third integer is 82. X + (X + 2) = 82 2X + 2 = 82 2X = 80 X = 40 40, 41, 42

18. Example 10 • Find three consecutive even integers whose sum is 426. The three integers are 140, 142, and 144

19. Example 11 • George is five cm taller than John. The sum of the heights is 405 cm. How tall is George? Then you can write your equation and solve What are we looking for? Let George be our variable, x Then define John in terms of George. John = x-5 George is 205 cm.

20. Example 12 • The Lions played twenty seven basketball games. They won twice as many as they lost. How many did they win? Let the number they lost be x Number they won =2x The Lions won 18 games.

21. Example 13 • Find three consecutive odd integers whose sum is 33 9, 11, 13