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

Answer:

x=20 and y=16

Step-by-step 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:

$\frac{1x}{2}+\frac{1y}{2}=18$           (2)

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

$\frac{4+y}{2}+\frac{y}{2}=18$

After simplification by taking LCM of the fraction we get:

$\frac{4+y+y}{2}=18$

After further simplification we get:

$\frac{4+2y}{2}=18$

$2y=32$

$\Rightarrow y=16$

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

x=4+16=20

Hence, x=20 and y=16