Question

Mira picked two numbers from a bowl. The difference of the two numbers was 4, and the sum of one-half of each number was 18. The system that represents Mira’s numbers is below. x – y = 4 1/2x + 1/2 y = 18 Which two numbers did Mira pick?

Answer 1

Answer: C.)(20, 16)

Explanation:

Answer 2

Well, we know that:

1/2(x) + 1/2(y) = 18

2( 1/2(x) + 1/2(y) ) = 2( 18 )

x + y = 36

and

x - y = 4

if we add y to both sides of x - y = 4, we get x = 4 + y. We can substitute that into our first equation.

4 + y + y = 36

subtract 4 from both sides and add like terms:

2y = 32

Divide both sides by 2:

y = 16

Substitute this into our second equation:

x - 16 = 4

Add 16 to both sides:

x = 20

We can check this by Substituting x with 20 and y with 16:

20 + 16 = 36

It checks out!

x = 20

y = 16