Question

One number is equal to two times a second number. Two times the first number plus two times the second number is 24. If you let x stand for the first number and y for the second, what are the two numbers?

A. x = 24, y = 12
B. x = 12, y = 6
C. x = 8, y = 4
D. x = –24, y = –12

Answer 1

1 number is 2 times second number
x is 2 times y
x=2y
2 times first plus 2 times second is 24
2x+2y=24

x=2y
sub
2x+x=24
3x=24
divide 3
x=8
sub
x=2y
8=2y
divide 2
4=y


x=8
y=4

C is answer

Answer 2

Option C is correct x=8 and y=4

Explanation:

We have been given two numbers first number is x and second number is y

From first case one number is equal to two times a second number we will get

`x=2y` (1)

From second case two times the first number plus two times the second number is 24 we will get

`2x+2y=24` (2)

On solving equation (1) and (2) by substituting
`x=2y` in equation (2) we will get

`2(2y)+2y=24`

After simplification we will get

`4y+2y=24`

`\Rightarrow 6y=24`

`\Rightarrow y=4`

Now, substitute
`y=4\text{in} x=2y` we will get

`\Rightarrow x=2(4)=8`

Therefore, Option C is correct x=8 and y=4