The sum of two numbers is 4 1/8 and their difference is 7/8. What are the numbers? Explain how you found your answer.

Question

asked Mar 7, 2021 158k views

1 Answer

Miriam · Answer 1 · 2021-03-11T19:12:26+0000

Answer:

x=3

y=(17)/(8)

Explanation:

Firstly, we have to transform what is written in words to equations.

The sum of two numbers is 41/8

If we call the unknown numbers as
and
, we will have:

x+y=(41)/(8) (1)

Their difference is 7/8

x-y=(7)/(8) (2)

Now we have a system with two equations and two unknowns. Let's solve it.

Isolating
from (1):

x=(41)/(8)-y (3)

Substituting (3) in (2):

(41)/(8)-y-y=(7)/(8) (4)

Isolating
:

(41)/(8)-(7)/(8)=2y

y=(34)/(16)=(17)/(8) (5) This is the value of y

Substituting (5) in (1):

x+(17)/(8)=(41)/(8) (6)

Finding
:

x=(41)/(8)-(17)/(8)

x=3 (7) This is the value of x