Solve by elimination

Question

for a school band trip, Mercier decides to order T-shirts for all the participants. It will cost four dollars per shirt for the medium size, and five dollars per shirt for the large size. Marsia orders a total of 70 T-shirts and spends $320. How many or medium shirt?

Answer 1

Step 1: Write the equations. In this case, let "m" be the number of size medium shirts she orders and let "l" be the number of size large shirts she orders. So, m + l = 70 and (for the cost) 4m + 5l = 320

Step 2: Write the equations over the top of one another and look for a variable to eliminate:

m + l = 70

4m + 5l = 320

If I multiply the first equation by -4, I can eliminate the m variable by adding the equations together.

Step 3: Modify the equations and put the modified equations over each other and add them together. In this case I'm going to multiply the first equation by -4 and list that as the new first equation:

-4m - 4l = -280

4m + 5l = 320

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l = 40

Step 4: Plug the solution back into the easiest of the equations to solve for the other variable. In this case the easiest is m + l = 70 so:

m + 40 = 70 or m = 30