math

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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?

  • math -

    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~ :)

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