Question 1167518: Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
The Arlington Tigers are having team shirts made. One option is to pay Justin's Tees a $35 setup fee and then buy the shirts for $10 each. Another option is to go to City Printing, paying $25 for a setup fee and an additional $12 per shirt. The team parent in charge of the project notices that, with a certain number of shirts, the two options have the same cost. How many shirts is that? What is the cost?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! your 2 equations are:
c = 35 + 10x
c = 25 + 12x
c is the total cost.
x is the number of shirts.
to solve by substitution, solve for one of the variables using one of the equations and then replace that variable in the other equation by the equivalent value you derived from one of the equations.
in this problem, you would solve for c in the first equation.
since it is already solved for c, you have no additional work to do except to replace c in the second equation with its equivalent value of 35 + 10x you derived from the first equation.
you get 35 + 10x = 25 + 12x
subtract 25 from both sides of the equation and subtract 10x from both sides of the equation to get 10 = 2x
solve for x to get x = 5
when x = 5, c = 35 + 10x becomes c = 85 and c = 25 + 12c becomes c = 85.
the value of x in both equations is equal to 85 which is what you want.
that occurs when x = 5.
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