Algebra 1 Word Problem

Question

Separate the number 92 into two parts. When one part is divided by the other part, the result is 4 with a remainder of 2. What is the fraction formed by two parts?

Answer 1

92=x+y

x/y=4r2

74/18=4r2

Answer 2

"Separate 92 into two parts" must mean addition. If it were multiplication, they would have used the word "factors" instead of "parts".

Given:

a + b = 92 [let the parts be a and b]

a/b = 4 rem 2

This means that a = 4b +2

a - 4b = 2

a + b = 92 [first equation]

a - 4b = 2 [second equation]

------------------------- [solve by elimination; subtract equations]

5b = 90

b = 18

Since a + b = 92, then a=74

Check:

Does 74 + 18 = 92 ? yes

Does 74/18 = 4 rem 2 ? yes