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: (96)
B. 2x + y = 24
2x - y = 12
Solution: (96)
C. 2(x + y) = 24
2x - y = 12
Solution: (6,9)
D. 2x + y = 24
2(x - y) = 12
Solution: (6,9)
Please hurry !

Answer 1

B

Explanation:

Let first number = x

Second number = y

Twice a number = 2*x = 2x

The sum of twice a number and another number is 24

2x + y = 24 -----------------------(I)

The difference of twice the first number and the other number is 12.

2x - y = 12 ----------------------(II)

Add equation (I) & (II) and y will be eliminated and we can find the number 'x'

(I) 2x + y = 24

(II) 2x - y = 12 {Now add the two equations}

4x = 36

Divide both sides by 4

4x/4 = 36/4

x = 9

Plug in the value of 'x' in equation (I)

2*9 + y = 24

18 + y = 24

Subtract 18 from both sides

18 + y - 18 = 24 - 18

y = 6

The numbers are 9, 6