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You have three unknowns in this word problem.

LET X = NUMBER OF Hot Dogs YOU EAT AT 16 SECONDS PER DOG

LET Y = NUMBER OF HOT DOGS YOUR FRIEND EATS AT 22 SECONDS PER DOG

LET Z = TIME IT TAKES TO EAT 38 HOT DOGS

Since there are 3 unknowns you need 3 equations to solve them

YOU KNOW THAT

1. X + Y= 38 (total dogs)

2. 16X = 22 Y (since they spend same time eating, times are equal)

3. 16X + 22Y = Z (total time)

SOLVE FOR Y in (2) in terms of X; plug in and solve for X in (1)

Plug back into (2) to solve Y

Solve Z in (3) using X and Y

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