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 x + y = 18 Which two numbers did Mira pick? (10, 8) (18, 4) (20, 16) (40, 32)

Answer 1

(20, 16), they are the only two numbers that have a difference of 4 and take half of each of those numbers and add them together it will equal 18.

Hope this helped :)

Answer 2

Answer: The correct option is (C) (20, 16).

Step-by-step explanation: Given that 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.

We are to find the two numbers that Mira pick.

Let a and b be the two numbers that Mira pick.

Then, according to the given information, we have

`x-y=4~~~~~~~~~~~~~~~~~~~~~~(i)\\\\(1)/(2)(x+y)=18~~~~~~~~~~~~~~~~(ii)`

From equation (i), we have

`x-y=4\\\\\Rightarrow x=y+4~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)`

Substituting the value of x from equation (iii) in equation (ii), we get

`(1)/(2)(x+y)=18\\\\\Rightarrow x+y=36\\\\\Rightarrow y+4+y=36\\\\\Rightarrow 2y=32\\\\\Rightarrow y=(32)/(2)\\\\\Rightarrow y=16.`

Now, from equation (iii), we get

`x=y+4=16+4=20.`

Thus, the two numbers that Mira pick are 20 and 16.

Option (C) is CORRECT.