Math Problem

Question

Mr. Green bought dinner home to his family from the local fast food restaurant. He brought hotdogs, which sell for $1.50 each and hamburgers, which sell for $2.00 each. If he brought a total of 8 hamburgers and hotdogs, and he spent $14.50, how many hamburgers and how many hotdogs did he purchase?

Answer 1

Let d  = number of hotdogs

Let b = number of burgers

 

8 total so

 

b + d = 8

 

Total cost was $14.50 so

 

1.5d + 2b = 14.50

 

Solve for b in the first equation to get b = 8 - d

 

Substitute this expression for b into the second equation.

 

1.5d + 2b = 14.50 becomes 1.5d + 2(8 - d) = 14.50

 

Now we have an equation with a single variable so solve for d

 

1.5d + 16 - 2d = 14.50

 

-0.5d + 16 = 14.50

 

-0.5d = -1.50

 

d = 3

 

If d = 3, then b = 5