Solving a Hot Dog Word Problem with a Linear Equation

by Paula Austin
(Midland, North Carolina )

Shawn was training for a hot dog contest. He trained for 6 days and each day he ate 4 more hot dogs. At the end of 6 days he had ate 150 hot dogs. How many did he eat each day?

Let x be the amount of hot dogs he ate on day 1

On day 2, he ate x + 4

On day 3, he ate x + 4 + 4 = x + 8

On day 4, he ate x + 4 + 4 + 4 = x + 12

On day 5, he ate x + 4 + 4 + 4 + 4 = x + 16

On day 6, he ate x + 4 + 4 + 4 + 4 + 4 = x + 20

Amount on day 1 + amount on day 2 + amount on day 3 + amount on day 4 + amount on day 5 + amount on day 6 = 150

x + x + 4 + x + 8 + x + 12 + x + 16 + x + 20 = 150

6x + 60 = 150

6x + 60 - 60 = 150 - 60

6x + 0 = 90

6x = 90

6x / 6 = 90 / 6

x = 15

So on day 1, he ate 15 hot dogs.

On day 2, he ate 19 hot dogs.

On day 3, he ate 23 hot dogs.

On day 4, he ate 27 hot dogs.

On day 5, he ate 31 hot dogs.

Finally, on day 6, he ate 35 hot dogs.

Indeed, 15 + 19 + 23 + 27 + 31 + 35 = 150