Question

If one number is five more than another number, and the smaller number is half of the larger number, what are the two numbers?

Answer 1

10 and 5

Explanation:

Let the first number be x.

Let the second number be y.

x = 5 + y

y = 1/2x

Plug y as 1/2x in the first equation.

x = 5 + (1/2x)

Solve for x.

Subtract 1/2x on both sides.

x - 1/2x = 5 + 1/2x - 1/2x

1/2x = 5

Multiply both sides by 2.

2(1/2x) = 2(5)

x = 10

Plug x as 10 in the second equation.

y = 1/2(10)

Solve for y.

y = 5

x = 10

y = 5

The two numbers are 10 and 5.

10 is the larger number.

5 is the smaller number.

Answer 2

Larger number = 10

Smaller number = 5

Explanation:

Let larger number be x

Let smaller number be y

`x = 5 + y`---> equation (i)

`y = (1)/(2) x`

`x = 2y`-----> equation (ii)

Equate equation (i) and (ii),

`5 + y = 2y`

Move variable to L.H.S and change its sign:

Similarly, Move constant to R.H.S and change its sign

`y - 2y = - 5`

`- y = - 5`

The difference sign (-) will be cancelled on both sides

`y = 5`

Putting the value of y in equation (ii) in order to find the value of X ( larger number)

`x = 2y`

Plug the value of y

`= 2 * 5`

Calculate the product

`= 10`

Hence,

Smaller number = 5

Larger number = 10

Hope this helps..

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