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
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
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
To solve this problem, let's break it down step by step.
Let's denote the number of teddy bears in the first store as 'x' and the number of teddy bears in the second store as 'y'.
According to the problem, the two stores have a combined total of 210 teddy bears, so we can write the equation: x + y = 210 (Equation 1)
After the first store sold 1/2 of its teddy bears, it would have (1 - 1/2) = 1/2 of its original number of teddy bears left. Similarly, the second store would have (1 - 1/3) = 2/3 of its original number of teddy bears left.
Since both stores have the same number of teddy bears left, we can write the equation: (1/2)x = (2/3)y (Equation 2)
Now we have a system of equations consisting of Equation 1 and Equation 2. To solve for the unknowns x and y, we can use various methods such as substitution or elimination.
Let's solve it using the substitution method:
From Equation 2, we can rewrite it as x = (2/3)y * (2/1), which simplifies to x = (4/3)y.
Now we substitute this value for x in Equation 1:
(4/3)y + y = 210
(7/3)y = 210
Multiply both sides by 3/7 to isolate y:
y = (210 * 3/7)
y = 90
Now substitute the value of y back into Equation 1 to find x:
x + 90 = 210
x = 210 - 90
x = 120
So the number of teddy bears in the first store (x) is 120 and the number of teddy bears in the second store (y) is 90.
To find the number of teddy bears sold from the two stores combined, simply subtract the number of teddy bears left in each store from their original quantities:
From the first store: (1/2)x = (1/2) * 120 = 60
From the second store: (1/3)y = (1/3) * 90 = 30
Therefore, the number of teddy bears sold from the two stores combined is 60 + 30 = 90.