Question

A dormitory manager buys 38 bed sheets and 61 towels for $791.50. The manager get another 54 bed sheets and 50 towels for $923 from the same store. What is the cost of one bed sheet and one towel?

Answer 1

38b + 61t = 791.50....multiply by 27
54b + 50t = 923.....multiply by -19
-------------------
1026b + 1647t = 21370.5 (result of multiplying by 27)
-1026b - 950t = - 17537 (result of multiplying by -19)
------------------add
697t = 3833.50
t = 3833.50 / 697
t = 5.50 <=== cost of each towel

38b + 61t = 791.50
38b + 61(5.50) = 791.50
38b + 335.50 = 791.50
38b = 791.50 - 335.50
38b = 456
b = 456/38
b = 12 <== cost of each bed sheet

so the cost of 1 towel and 1 bed sheet is : 12 + 5.50 = 17.50