Question

Savanna is playing a game with her friends. She tells them to each pick a number, and then she directs them to: 1. Multiply their number by 4 2. Subtract 6 from that number 3. Divide that number by 2. Once they do that, they each tell Savanna their number a. Arturo says his "new" number is -15. What number did Arturo start with? b. Summer says her "new" number is 18. What number did Summer start with?c. Ryan says his "new" number is 199. What number did Ryan start with?

Answer 1

a) -6

b) 10.5

c) 101

Explanation:

Let x represent the number that they picked.

1. Multiply their number by 4

x × 4 = 4x

2. Subtract 6 from that number

4x - 6

3. Divide that number by 2.

(4x -6)/2

a) Arturo says his "new" number is -15.

(4x -6)/2 = -15

Solving for x.

4x -6 = 2 × -15

4x = -30 + 6 = -24

x = -24/4 = -6

b) Summer says her "new" number is 18

(4x -6)/2 = 18

Solving for x

(4x-6) = 18 × 2 = 36

4x = 36 + 6 = 42

x = 42/4 = 10.5

c) Ryan says his "new" number is 199

(4x -6)/2 = 199

Solving for x

4x -6 = 199×2 = 398

4x = 398+6= 404

x = 404/4 = 101