Correct value of x?

Question

The larger of two numbers is five less than twice the smaller number. The sum of four times the larger and twice the smaller number is 100. If X is the smaller number which equation below determines the correct value of X?

Answer 1

There was no choice of equation to choose from.

But I'll show how to find the answer.

Let Y > X.

Y = 2X - 5 (two times the smaller, less 5)

4Y + 2X = 100 (four times larger plus 2 time smaller = 100)

But Y = 2X - 5 from above, so

4(2X-5) + 2X = 100

8X - 20 + 2X = 100

10X = 120

X = 12.

Check: 2X = 2*12 = 24

4Y = 4(2X-5) = 8*12 - 20 = 96 - 70 = 76

Y = 19

Note 76+24 = 100.

Answer 2

y=2x-5

4y+2x=100

Subtract the first equation from the second

3y=105

Can you go on from here if required?

Answer 3

Let Y be the larger number and X be the smaller number. From the question two equations can be written:

(1) . Y = 2X - 5

(2) . 4Y + 2X = 100

From the first equation, Y can be substituted in the second equation as follows:

4(2X -5) + 2X =100

this can be rearranged to solve for X

8X -20 + 2X = 100

10X = 120

X can be determined by X = 120/10 . = 12

Y can also be found by substituting back into equation 1for X

Y = 2 * 12 -5 = 19