The students at Jefferson middle school are raising money for a charity by selling t shirts and hats. The number of t shirts sold was 3 times the number of hats. The profit was 5 dollars for each t shirt sold and 2.50 dollars for each hat sold. The students raised 840 dollars for the charity. They used the system below to analyze their success and found the solution

144 t-shirts and 48 hats.

Step-by-step explanation:

Let's define:

T = number of t-shirts sold.

H = number of hats sold.

We know that:

"The number of t-shirts sold was 3 times the number of hats"

Then:

T = 3*H

We also know that the profit was $5 for each t-shirt and $2.50 for each hat, then the total profit is written as:

T*$5 + H*$2.50

And we know that the total profit is $840, then we have the equation:

T*$5 + H*$2.50 = $840

Then we have the system of equations:

T = 3*H

T*$5 + H*$2.50 = $840

To solve this, we already have a variable isolated in one of the equations (T), then we can just replace it in the other equation:

(3*H)*$5 + H*$2.50 = $840

Now we can solve this for H.

H*$15 + H*$2.50 = $840

H*$17.50 = $840

H = $840/$17.50 = 48

This means that there were sold 48 hats.

Now if we use the equation T = 3*H we can find the number of t-shirts sold

T = 3*48 = 144

There where 144 t-shirts sold.