Question

Two stores have a combined total of 210 teddy bears. After the first store sold 1/2 of its teddy bears and the second store sold 1/3 of its teddy bears, each store had the same number of teddy bears left. How many teddy bears were sold from the two stores combined?

What would the equation be? x=numbers of teddy bears sold

Answer 1

let
x = # in 1st store
y = # in 2nd store

x + y = 210
x/2 = 2y/3
or
x + y = 210
3x = 4y, so y = 3/4 x
x + 3/4 x = 210
7/4 x = 210
x = 120
so, y = 90

1/2 of 120 = 60
1/3 of 90 = 30
so, 90 bears were sold

Answer 2

I would need to use a strip diagram. The first store will be 2/4 instead of 1/2 since the store sold 1/2 and then the second store will be 2/3 since the store sold 1/3. Would the equation then be 2/3x + x = 210. Then, 5/3x = 210. Then, 210 times 3/5. X=126