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

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

$x-y=4~~~~~~~~~~~~~~~~~~~~~~(i)\\\\\dfrac{1}{2}(x+y)=18~~~~~~~~~~~~~~~~(ii)$

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

$\dfrac{1}{2}(x+y)=18\\\\\Rightarrow x+y=36\\\\\Rightarrow y+4+y=36\\\\\Rightarrow 2y=32\\\\\Rightarrow y=\dfrac{32}{2}\\\\\Rightarrow y=16.$

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.

Answer 2

(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 :)