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)
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B

Step-by-step 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

answer:

step-by-step explanation:

step-by-step explanation:

the ratio of red paint to blue paint is always 9/7. that means that, whatever x's value, (4x+12)/(4x-4) has that same ratio. so, set up an equation and cross-multiply to solve for x:

9/7 = (4x+12)/(4x-4)

9(4x-4) = 7(4x+12)

36x - 36 = 28x + 84

8x - 36 = 84

8x = 120

x = 15