Greetings! Would like assistance with the following if possible:
A shop sells both formal gowns and novelty tshirts. The formal gowns run $500 per dress. The tshirts sell for around $12 each. If the store sold 700 items and made a profit of $23,040, then how many of each was sold?
How do you approach this type of problem?
Thank yoU!
Posted on Apr 13, 2017, by Mcdanie1 
Posted on Apr 13, 2017, by
Talanab

Hello! First set up equations using what we know, and what we don't know (variables).
We don't know how many dresses were sold, so let's say D=number of dresses sold.
We don't know how many tshirts were sold, so let's say T=number of tshirts sold.
We know that the number of dresses sold plus the number of tshirts sold totaled 700, so we can make our first equation:
D+T=700.
We also know that they sold D number of dresses for $500 each, plus T number of tshirts for $12, and the total profit was $23,040. We can make another equation with that:
500D+12T=23,040
Now we have two equations and we have to solve them. The easiest way is to isolate one variable in the first equation. Here's what I mean:
D+T=700
subtract T from each side
D=700T
Now you can use that in the other equation.
Replace D with 700T so that you can solve for T.
500D+12T=23,040
500(700T)+12T=23,040
Multiply that out and simplify:
350,000500T+12T=23,040
350,000488T=23,040
Now begin to get the T alone on one side by subtracting 350,000 from each side:
488T=326,960
Get the T alone on one side by dividing each side by 488:
T=670
Now insert that number into the very first equation to solve for D.
D+T=700
D+670=700
D=30
You have solved for T and D, so you now know that there were 670 tshirts sold and 30 dresses sold.
You can always go back and check your work by putting those numbers back into any of the equations to see if they work out.
Hope this helps!