Linear Equations

Question

Milan sold t-shirts and hats at a festival. His total profit was $106 . He made a $4 profit for each t-shirt he sold. He also made a profit of $34 from selling hats. How many t-shirts did he sell?

Write an equation that could be used to answer the question above. First, choose the appropriate form. Then, fill in the blanks with the numbers 106 , 4 , 34 and . Let x represent the number of t-shirts.

Answer 1

4x + 34 = 106

4x + 34 - 34 = 106 - 34

4x = 72

x = 72/4

x = 18 t-shirts

Answer 2

This is a basic 2 step equation. The form used to solve this equation is ax + b = c. Based on the scenario:

a = $4

b = $34

c = $106

x = # of t-shirts sold

4x + 34 = 106

4x + 34 - 34 = 106 -34

4x = 72

x = 18 t-shirts

Answer 3

We are told total profit is $106, and Milan made $4 per shirt and $34 TOTAL from selling hats.

This is more of a one-variable equation:

4x + 34 = 106

4x = 72

x = 18

So, Milan sold 18 t-shirts. We are not told the unit price per hat he sold, so we could only guess, like for example they could've sold 2 hats for $17 or 17 hats for $2. Those are mere hypotheticals though.

Answer 4

4x + 34y = 106

x, y are whole numbers

x y

1 3

or

18 1

1 shirt,& 3 hats

4+3(34)=4+102=106

or

18 shirts & 1 hat

4(18)+34=72+34=106

There are an infinite number of possibilities, but the restriction of whole numbers narrows it down to just two