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~ :)

To solve this problem, we need to set up equations based on the given information.

Let's assume the cost of the pair of shoes as 'x'.

According to the problem, the bag cost $15 more than the pair of shoes. So, the cost of the bag would be 'x + $15'.

Also, the watch cost $20 less than the bag. Thus, the cost of the watch is '(x + $15) - $20'.

According to the problem, the total cost of the bag, pair of shoes, and the watch is $160. Thus, we can write the equation:

x + (x + $15) + ((x + $15) - $20) = $160

Now, we can solve this equation to find the value of 'x', which represents the cost of the pair of shoes.