Olivia has $180 to buy presents for her 3 sisters and 2 nephews. She wants to spend $15 more on each sister than she spends on each nephew. How much does she spend on each sister?

So

if x is the number she spent on each sister and y is the number she spent on each nephew then

180=3x+2y

she wants to spend 15 dollars more on sisters than nephews

so

x=15+y

solve

we have

180=3x+2y and

x=15+y

subsitute 15+y for x

180=3 (15+y) + 2y

180=45+3y+2y

180=45+5y

minus 45 both sides

135=5y

divide both sides by 5

27=y

solve for x

x=15+y

x=15+27

x=42

she spent $42 on each sister

3 (x + 15) + 2x = 180

3x + 45 + 2x = 180

3x + 2x = 180 - 45

5x = 135

x = 135/5

x = 27

27 + 15 = 42 ... on each sister <==

27 for each nephew