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Question

Mohammed and Ali are selling pies for a fundraiser Mohammed sold 3 small pies and 11 large pies for a total of 203 Ali sold 11 small pies and 11 large pies for a total of 220 Determine the cost each of one small pie and large pie.

Answer 1

Are you certain your problem is as written? I believe it should actually read, 3 small pies and 14 large pies (not 11) for 203, and 11 small and 11 large for 220. The way you had it written it has a solution that is sort of wonky. I will explain the solution to the one I have written here and it should help you!

Solving by substitution means solving two separate linear equations with 2 variables by arbitrarily solving one for a variable and substituting it into the other to solve it.

First, write two equations from the word problem:

3 small pies plus 14 large pies equals 203 dollars

11 small pies plus 11 large pies equals 220 dollars

3s + 14L = 203

11s + 11L = 220

Now we choose one to solve for a variable in. I choose the second because it has 11 and 220, which should divide out nicely. So I will “solve” for “s” in the second equation.

               11s + 11L = 220

               11s + 11L – 11L = 220 – 11L

               11s = 220 – 11L

               11s ÷ 11 = (220 – 11L) ÷ 11

               S = 20 – L

So now we have an expression to use in place of “s” in the other expression that will allow us to solve for “L” in it.

               3s + 14L = 203

               3(20 – L) + 14L = 203

               60 – 3L + 14L = 203

               60 + 11L = 203

               60 – 60 + 11L = 203 – 60

               11L = 143

               11L ÷ 11 = 143 ÷ 11

               L = 13

So we have now determined that a single large pie cost $13. We can use this in the original equations to find the price of the small pies.

3s + 14L = 203                                                    11s + 11L = 220

3s + (14 X 13) = 203                                          11s + (11 X 13) = 220

3s + 182 = 203                                                    11s + 143 = 220

3s + 182 – 182 = 203 – 182                            11s + 143 – 143 = 220 – 143

3s = 21                                                                11s = 77

s = 7                                                                    s = 7

So, Large pies cost $13 each and small pies cost $7 each according to our substitution method. Please let me know if you have any questions!