Question

Kevin and Brittany write an equation to represent the following relationship, and both students solve their equation. Who found the correct equation and solution? Why is the other person incorrect?

6 times the difference of a number and 20 is the same as half the sum of 8 more than 8 times a number.

Kevin: 6(x − 20) =
1
2
(8x + 8) 6x − 120 = 4x + 4 6x − 120 − 4x = 4x + 4 − 4x 2x − 120 = 4 2x − 120 + 120 = 4 + 120 2x = 124
2x
2
=
124
2
x = 62 Brittany: 6(20 − x) =
1
2
(8x + 8) 120 − 6x = 4x + 4 120 − 6x − 4x = 4x + 4 − 4x 120 − 2x = 4 120 − 2x − 120 = 4 − 120 −2x = −116
−2x
−2
=
−116
−2
x = 58

The incorrect solution expressed the
difference of a number and 20 incorrectly
.
Kevin's
expression
20 − x
was correct.

Answer 1

Kevin found the correct equation and solution, while Brittany made an error in expressing the difference of a number and 20.

Step-by-step explanation:

Kevin found the correct equation and solution. His equation is 6(x − 20) = 1/2(8x + 8), which simplifies to 6x − 120 = 4x + 4. When solving this equation, Kevin subtracts 4x from both sides to get 2x − 120 = 4. Then he adds 120 to both sides to get 2x = 124, and finally divides both sides by 2 to find x = 62.

Brittany, on the other hand, made an error when expressing the difference of a number and 20. Her equation is 6(20 − x) = 1/2(8x + 8), which simplifies to 120 − 6x = 4x + 4. However, instead of correctly subtracting 6x from both sides, she subtracts 4x, which leads to an incorrect solution of x = 58.