Question

The sum of twice a number and another number is 24. The difference of twice the first number and the other number is 12. Which system would model this situation, and what is the solution?
A. 2(x + y) = 24
2(x – y) = 12
Solution: (9, 6)
B. 2x + y = 24
2x – y = 12
Solution: (9, 6)
C. 2(x + y) = 24
2x – y = 12
Solution: (6, 9)
D. 2x + y = 24
2(x – y) = 12
Solution: (6, 9)

Answer 1

Call the first number x and the other number y.
"The sum of" means you add together items after whatever's been described for the individual items. It's like putting parentheses around the named items. "The difference of" is the same except you have a subtraction inside the parentheses.
"twice a number" means you multiply that one number by 2
"and the other number" means you do nothing to that other number except include it in the sum
"is" means =
So:
( 2x + y ) = 24
and
( 2x - y ) = 12
We can solve for x and y, or we can plug in the numbers given (x = 9, y = 6) and verify this yields the right answers of 24 and 12.

Answer 2

So A. ? Right?

Answer 3

Yep

Answer 4

Thank you:)

Answer 5

You're welcome :)