a sporting goods store sold twice as many t-shirts as shorts. T-shirts are $9 each, shorts are $14 each. The total amount of money taken in for both items was $256. find the number of each that was sold.
Please help
T=T-shirts
S=shorts
T= 2S
I know half as much shorts were sold and doubling the number of shorts would give me the number of t-shirts.
9T + 14S = 256
Because I know that T=2S, I could replace the T with 2S.
9(2S)+14S=256
By using substitution, I have one variable to work with.
Solve for s to find the number of shorts sold.
Then, you can plug it back into T=2S and solve for T to find the number of T-shirts sold.
To find the number of t-shirts and shorts that were sold, we can set up a system of equations based on the given information.
Let's assume the number of shorts sold is 'x'.
According to the problem, the number of t-shirts sold is twice the number of shorts sold, so the number of t-shirts sold would be '2x'.
The cost of each t-shirt is $9, so the total cost of t-shirts sold would be 9*(2x) = 18x.
The cost of each short is $14, so the total cost of shorts sold would be 14*x = 14x.
The total amount of money taken in for both items was given as $256, so we can set up the equation:
18x + 14x = 256
Combining like terms, we get:
32x = 256
Dividing both sides by 32, we find:
x = 8
Therefore, the number of shorts sold is 8.
Since the number of t-shirts sold is twice the number of shorts sold, the number of t-shirts sold would be 2*8 = 16.
So, 16 t-shirts and 8 shorts were sold.