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. 1/2x – 1/2y = 4 x + y = 18 Which two numbers did Mira pick?

Answer 1

multiply 1/2x - 1/2 y = 4 by 2,, we get x - y = 8

x - y = 8 and
x + y = 18 Adding these 2 equations:-

2x = 26
x = 13

and y = 18-13 = 5


Mira picked the numbers 13 and 5.

Answer 2

x=20 and y=16

Explanation:

Let the two numbers be x and y

Difference of two numbers was 4 that is:

`x-y=4` (1)

And sum of one-half of each number was 18 that is:

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

For solving equation (1) and (2) we substitute x=4+y in equation (2) we get:

`(4+y)/(2)+(y)/(2)=18`

After simplification by taking LCM of the fraction we get:

`(4+y+y)/(2)=18`

After further simplification we get:

`(4+2y)/(2)=18`

`2y=32`

`\Rightarrow y=16`

Now, substitute y=16 in x=4+y we get:

x=4+16=20

Hence, x=20 and y=16