Bill and Rosa have only nickels and dimes. Rosa has 75 cents and Bill has 90 cents. Each has the same number of coins and Bill has the same number of dimes as Rosa has nickels.How many nickels does Rosa have?

Answer 1

Rosa:
number of dimes --- x
number of nickels ---- y

Bill:
number of dimes --- y
number of nickels --- x, must be x because they both have x+y coins

Rosa's equation: 10x + 5y = 75 , or
2x + y = 15

Bill's equation: 5x + 10y = 90 , or
x + 2y = 18 ====> x = 18-2y

plug Bill's into Rosa's
2(18-2y) + y = 15
36 - 4y + y = 15
y = 7
in my head, x = 4

state your conclusion