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

Option B. is correct

2x + y = 24.

2x – y = 12.

Solution: (9, 6).

Explanation:

Let the first number be x and another number be y.

As per the statement:

"The sum of twice a number and another number is 24" translated to

`2x+y = 24`

It is also given that:

"The difference of twice the first number and the other number is 12" translated to

`2x-y = 12`

The system would model this situation:

`2x+y = 24` ....[1]

`2x-y = 12` ....[2]

Add equation [1] and [2] we get;

`4x = 36`

Divide both sides by 4 we have;

x = 9

Substitute in [1] we have;

2(9)+y = 24

18+y = 24

Subtract 18 from both sides we get;

y = 6

Solution = (9, 6)

Therefore, the system would model this situation:

`2x+y = 24`

`2x-y = 12`

and the solution is, (9, 6)

Answer 2

The answer is B. 2x + y = 24 ; 2x - y = 12. Solution: (9,6)

This is easily answered by translating the given worded statements into their mathematical form. Sum refers to the addition of two terms, and difference refers to the subtraction of two terms.

Substituting the given solution set, the equations are proven to be correct.