Dots sells t-shirts ($2) and shorts ($4). In April total sales were $456. People bought 4 times as many t-shirts as shorts. How many t-shirts and shorts did Dots sell?

Dots sold 152 t-shirts and 38 shorts sold.

Step-by-step explanation:

Let t = t-shirts and s = shorts.

We know that people bought 4 times as many t-shorts as shorts, which can be set to the equation t = 4s

Since t-shirts cost $2, shorts cost $4, and the total sales was $456, we can set the equation 2t + 4s = 456

So our two equations are:

t = 4s

2t + 4s = 456

Substitute t from the 1st equation into the 2nd:

2 (4s) + 4s = 456

8s + 4s = 456

12s = 456

s = 38

There were 38 shorts sold.

Since we have the number of shorts, we can plug that back into the 1st equation to find the number of t-shirts sold:

t = 4s

t = 4 (38)

t = 152

There were 152 t-shirts sold.