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: 2/3x + x times 1/2 = 210. Then, 5/3x times 1/2 = 210 times 2/1. 5/3x = 420. X= 252. Then 252-210 = 42
I don’t know if I’m correct
well, did you check you answer to see whether it worked out?
I did and it doesn’t. I know the answer is 105, but don’t know what the equation is
Store #1 has X teddy bears.
Store #2 has Y teddy bears.
Eq1: x + y = 210.
Eq2: x/2 = 2y/3.
X = 4y/3.
In Eq1, replace X with 4y/3 and solve for Y:
4y/3 + y = 210.
4y + 3y = 630,
Y = 90.
x + y = 210.
x + 90 = 210,
X = 120.
1/2 * 120 = 60 sold by store #1.
1/3 * 90 = 30 sold by store #2.
60 + 30 = 90 = Combined total sold by the 2 stores.
Your attempt to solve the problem and find the answer is partially correct. Let me guide you through the correct steps.
First, we can set x as the initial number of teddy bears in the first store. Since the combined total of teddy bears in both stores is 210, the second store must have had 210 - x teddy bears.
After the first store sold half of its teddy bears, it would have (1/2)x teddy bears remaining. Similarly, after the second store sold one-third of its teddy bears, it would have (2/3)(210 - x) teddy bears remaining.
According to the problem statement, both stores ended up with the same number of teddy bears left. So, we can equate the two expressions:
(1/2)x = (2/3)(210 - x)
Now, let's solve this equation to find the value of x.
Start by multiplying both sides of the equation by the least common multiple of the denominators, which is 6:
6 * (1/2)x = 6 * (2/3)(210 - x)
3x = 4(210 - x)
Distribute 4 to both terms inside the parentheses:
3x = 840 - 4x
Combine like terms:
3x + 4x = 840
7x = 840
Divide both sides of the equation by 7 to isolate x:
x = 840 / 7
x = 120
Now, substitute this value of x back into one of the original expressions to find the number of teddy bears sold from the two stores combined:
Number of teddy bears sold = (1/2)x + (2/3)(210 - x)
Number of teddy bears sold = (1/2)(120) + (2/3)(210 - 120)
Number of teddy bears sold = 60 + (2/3)(90)
Number of teddy bears sold = 60 + 60
Number of teddy bears sold = 120
Therefore, the number of teddy bears sold from the two stores combined is 120.