what is my equation?

Question

A school is organizing a cookout where hotdogs will be served. The hotdogs come in small packs and large packs. Each small pack has 8 hotdogs and each large pack has 18 hotdogs. The school bought 13 packs of hotdogs that have a total of 164 hotdogs. Determine the number of small packs purchased and the number of large packs purchased. Put your answer as a coordinate pair (#small packs,#large packs) *

Answer 1

Hello Mia,

To solve this question, lets lay out the information:

We have 164 Hot-dogs

We have 13 packs of Hot-dogs

A small pack has 8 Hot-dogs

A large pack has 18 Hot-dogs

The question is what is the number of small/large packs purchased?

To be honest, right now I have no idea how many small packs or large packs the school bought. Let's say the school bought "x" amount of small packs and "y" amount of large packs ("x" and "y" represent the amount of small and large packs)

We can then write an equation like this:

8x + 18y = 164 equation (1)

We also know FOR A FACT, x + y = 13. Why? Because our small packs + our large packs = 13 packs of Hot-dogs

We can then write: x + y =13 ------> x = 13 - y equation (2)

Ahhhh and now we can substitute the "x" value in our other equation (1)

8x + 18y = 164------> 8(13 - y) + 18y = 164 ------> 104 - 8y + 18y = 164 -------> 10y = 60 ------> y = 6

There we go! y = 6, and then using equation (2) ----> x = 13 - 6 = 7; so x = 7

Let's check... 8*7 = 56 18*6 = 108 56 + 108 = 164

Our final answer is the school purchased 7 small packs of Hot-dogs and 6 large packs of Hot-dogs

(x,y) = (7,6)

Answer 2

You equation is:

8(x) + 18(13 - x) =164

Can you solve for x and answer?