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? By using the strip diagram, 1/2 will still be 1/2, then 1/3 will be 2/3. So, the equation will be 1/2x + 2/3x = 210. Then 7/6x = 210. Then, 6/7 times 7/6x = 210 times 6/7. X=180. Then, 210-180=30.
yet again?
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
Again, we are not supposed to do it that way
I don't know what this strip diagram is supposed to be, but the equation you need is not
1/2x + 2/3x = 210
There were 210 bears to start with
1/2x + 2/3x is the number that remain after the sales were done.
I’m not sure how you got that equation you had
To solve this problem, we can follow these steps:
1. Let's assume the number of teddy bears in the first store is represented by x.
2. Since the first store sold 1/2 of its teddy bears, the number of teddy bears remaining in the first store is (1 - 1/2)x = 1/2x.
3. Similarly, let's assume the number of teddy bears in the second store is represented by y.
4. Since the second store sold 1/3 of its teddy bears, the number of teddy bears remaining in the second store is (1 - 1/3)y = 2/3y.
5. According to the given information, the number of teddy bears remaining in both stores is the same. Therefore, we have the equation: 1/2x = 2/3y.
6. The combined total of teddy bears in both stores is 210, so we also have the equation: x + y = 210.
7. Equating the two equations, we get: 1/2x = 2/3y = 210.
8. To simplify the equation, we can clear the fractions by multiplying both sides by 6 to eliminate the denominators: 3x = 4y.
9. Now, we can substitute x = 210 - y from the second equation into the first equation: 3(210 - y) = 4y.
10. Solving this equation, we get: 630 - 3y = 4y.
11. Combining like terms, we get: 630 = 7y.
12. Dividing both sides by 7, we find that y = 90.
13. Substituting this value of y back into the second equation, we find: x + 90 = 210.
14. Solving for x, we get: x = 120.
15. Finally, we can calculate the number of teddy bears sold by subtracting the remaining teddy bears from the initial total: (1/2x) + (2/3y) = (1/2 * 120) + (2/3 * 90) = 60 + 60 = 120.
Therefore, a total of 120 teddy bears were sold from the two stores combined.