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

Answer:

Larger number = 10

Smaller number = 5

Step-by-step explanation:

Let larger number be x

Let smaller number be y

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

$y = \frac{1}{2} x$

$x = 2y$-----> 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

$= 2 \times 5$

Calculate the product

$= 10$

Hence,

Smaller number = 5

Larger number = 10

Hope this helps..

Best regards!!

Answer 2

Answer:

10 and 5

Step-by-step 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.