Algebra 1 Word Equation

Question

A school sells t-shirts for $8 and sweatshirts for $12. If the total amount sold is 37 items and there is a $376 profit, how many sweatshirts and tshirts were sold?

Answer 1

Hi Nathan,

Let t= t shirt and s= sweatshirt

Keep the money items together in one equation and the amount

sold in another equation.

 

8t + 12s= 376  Equation 1

  

  t  + s = 37     Equation 2

 

You can solve this by elimination , for example multiplying the

second equation by -8, or by substitution  t= 37 -s and plugging this into the first equation

 

This should get you started. Let me know if you need further

assistance

Answer 2

There are two unknowns, so you'll need two equations.

From the problem statement, you know enough to calculate two different quantities.

1) The total number of shirts,

2) The total cost.

 

Call the numbers of shirts T and S.

The total number of shirts is the sum of T and S.

1) T + S = 37

The cost of the T-shirts is 8T

The cost of the Sweatshirts is 12S.

The total cost is the sum of these two.

2) 8T + 12S = 376

 

Now you have two equations and you can solve them using elimination or substitution.  I'll use elimination.

The idea is to eliminate one of the variables.

Multiply the first equation by (-8).  That will let us eliminate the T.

 

-8T - 8S = -296

  8T + 12S = 376    Add the second equation

             4S = 80

             S = 20

 

Substitute 20 for S in either equation and solve for T.

1) T + S = 37

T + 20 = 37

T = 17

 

Answer 3

Let T be the number of tee shirts sold

and S be the number of sweatshirts sold

 

8T + 12S = 376     (1) ($376 "profit" )

T + S = 37            (2) (37 items sold)

 

 

Multiply (2) by 8:

8T + 8S = 296

Subtract this result from (1):

0T + 4S = 80

 

Solve for S:

S = 80/4 = 20  

 

Use (2) to find T (eq 1 would also work, eq 2 is a bit simpler):  T + 20 = 37 —> T=37-20=17

 

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Ans:   17 tee shirts and 20 sweatshirts were sold. 

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Check:  8T+12S = 8(17) + 12(20) = 136 + 240 = 376 (ok)