SOLUTION: Darryl spent $55 on shirts. Tee shirts cost $5 and kind sleeve shirts cost $8. If he brought a total of 8 then how many of each kind did he buy? Write your answer using a complete

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Question 1137930: Darryl spent $55 on shirts. Tee shirts cost $5 and kind sleeve shirts cost $8. If he brought a total of 8 then how many of each kind did he buy? Write your answer using a complete sentence.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52852)   (Show Source): You can put this solution on YOUR website!
.
Let x = # of t-shirts, y = # of  sleeve shirts.


From the condition, you have these 2 equations


         x +    y =  8        (1)    (counting shirts)

       5*x +  8*y = 55        (2)    (counting money)
 

From equation (1), express  y = 8 - x  and substitute it into equation (2). You will get


       5x + 8*(8-x) = 55.


Express x and calculate answer


    x =  = 3.


Then from equation (1),  y = 8 - 3 = 5.


ANSWER.  3 t-shirts and 5 sleeve shirts.


CHECK.   3*5 + 5*8 = 55 dollars.   ! Correct !

The problem solved using 2-equation setup and the Substitution method.

--------------

This problem is similar to standard ticket problems.

For such problems,  read the lessons
    - Using systems of equations to solve problems on tickets
    - Three methods for solving standard (typical) problems on tickets
in this site.

From these lessons,  learn on how to solve such problems once and for all.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Systems of two linear equations in two unknowns".


Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


Note that, if a formal algebraic solution is not required, this problem can be solved very quickly with a little logical reasoning and some simple mental arithmetic.

The total cost of all the shirts is $55, which is a multiple of $5. The T-shirts cost $5 each; so the total cost of the t-shirts is a multiple of $5.

That means the total cost of the sleeve shirts has to be a multiple of $5. If they cost $8 each and the total cost of all the shirts was $55, then the number of sleeve shirts has to be 5.

So the 5 sleeve shirts cost 5($8) = $40, leaving $55-$40 = $15 for the t-shirts. At $5 each, the number of t-shirts he can buy for $15 is 3.

ANSWER: 5 sleeve shirts; 3 t-shirts.
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