math
posted by nick on .
john bought a bag, pai oh shoes ad a watch for $160 altogethe. the bag cost $15 more than the pair of shoes and the watch cost $20 less than the bag. What was the cost of the bag?

let x = cost of bag
let y = cost of shoes
let 160  (x+y) = cost of watch
set up equations:
(1) x = y + 15
(2) 160  (x+y) = x  20
solve simultaneously. we can either use elimination or substitution, but for this problem let's just use substitution. we substitute equation (1) to equation (2):
160  (y + 15 + y) = y + 15  20
160  2y  15 = y  5
2y  y = 160 + 15  5
3y = 150
y = $ 50 (cost of shoes)
x = y + 15 = $ 65 (cost of bag)
160  (x+y) = $ 45 (cost of watch)
hope this helps~ :)