Solve with substution

Question

Spongebob and Patrick are selling kelp fries to fundraise for new jellyfishing nets. They sold small and large sizes. Spongebob sold 3 small fries and 14 large fries for a total of $203. Patrick sold 11 small fries and 11 large fries for a total of $220. Find the cost of each size of fries.

Answer 1

Could also do substitution method as 2nd eqn boils down to S + L = 20. So S = 20 - L

3S + 14L = 203

3(20 - L) + 14L = 203

60 - 3L + 14L = 203

11L = 143

L = 143/11 = $13; S = 20 - 13 = $7

Answer 2

Let S = cost of small fries.

Let L = cost of. large fries.

3S + 14L = 203

11S + 11L = 220

First I will simplify by dividing 2nd equation by 11 to obtain

S + L = 20

Multiply by -3 and add to 2nd equation to eliminate S

-3S - 3L = -60

3S + 14L = 203

______________

11L = 143

L = 13

Using the first equation

3S + 14(13) = 203

S = 7

Check with the 2nd equation (always check your work and always use the other equation)

11(7) + 11(13) =? 203

77 + 144 = 220

220 = 220 check

Small fries cost $7 and large fries cost $13