On Monday, Jim spent $9.00 on 3 hot dogs and 2 cokes. On Tuesday, he spent $15.50 on 4 hot dogs and 5 cokes. What is the cost of a single hot dog and what is the cost of a single coke?

Answer 1

Let "h" be the cost of a hot dog and let "c" be the cost of a coke.

Both Monday's events and Tuesday's events must be true so the following equations BOTH must be true:

3h + 2c = 9.00

4h + 5c = 15.50

To solve these, there are several methods. I like to use elimination. To do that, we need to find a way to modify one or both of the equations so that when they are added together, one of the variables is eliminated.

Lets multiply the first equation bu -4 to get:

-12h - 8c = -36

Now lets multiply the second equation be 3 to get:

12h + 15c = 46.50

Now add the two equations together to eliminate the h's:

-12h - 8c = -36

12h + 15c = 46.50

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7c = 10.50

c = 10.5/7

c = 1.50

Then plug that value of c into either of the original equation, I'll choose the first. to get:

3h + 2(1.50) = 9.00

3h + 3.00 = 9.00

3h = 6.00

h = 2.00

So hot dogs cost $2.00 and cokes cost $1.50