A company sells T-shirts for $11 each and sweatshirts for $19 each.The number of T-shirts sold was 10 fewer than three times the number of sweatshirts sold. The T-shirts and sweatshirts sold for a total of $1,970. How many T-shirts were sold?

Question

A company sells T-shirts for $11 each and sweatshirts for $19 each.The number of T-shirts sold was 10 fewer than three times the number of sweatshirts sold. The T-shirts and sweatshirts sold for a total of $1,970. How many T-shirts were sold?

T-shirts

Answer 1

Let's call the number of sweatshirts sold "S" and the number of t-shirts sold "T". We know that the price of each t-shirt is $11 and the price of each sweatshirt is $19. We also know that the total revenue from selling t-shirts and sweatshirts is $1970.

From the information given, we can create two equations:

1) The number of t-shirts sold was 10 fewer than three times the number of sweatshirts sold.
T = 3S - 10

2) The total revenue from selling t-shirts and sweatshirts is $1970.
11T + 19S = 1970

We can now substitute equation 1 into equation 2 to solve for the number of t-shirts sold:

11*(3S-10) + 19S = 1970
33S - 110 + 19S = 1970
52S = 2080
S = 40

Now that we have the number of sweatshirts sold, we can substitute this value back into equation 1 to find the number of t-shirts sold:

T = 3*40 - 10
T = 110

So, 110 t-shirts were sold.