Question

Harold is buying packages of corndogs and hamburgers for a cookout. Harold bought 5 more packages of hamburgers than corndogs. A package of corndogs costs $2.00 and a package of hamburgers costs $5.00. Harold spent a total of $95.00. Write two equations. How many packages of hamburgers did Harold buy? How many packages of corndogs did Harold buy?

Answer 1

`y =x+5`

`2x+5 y = 95`

Number of packages of hamburgers bought = 15

Number of packages of corndogs bought = 10

Explanation:

Cost of a package of corndogs = $2.00

Cost of a package of hamburgers = $5.00

Let number of packages of corndogs bought =
`x`

Let number of packages of hamburgers bought =
`y`

Number of packages of hamburgers bought are 5 more than the cordogs.

The first equation can be written as:

`y =x+5 ..... (1)`

Total money spent = $95.00

Money spent on corndogs = Price of one package of corndogs
`*` Number of packages of corndogs bought = $2
`x`

Money spent on hamburgers = Price of one package of hamburgers
`*` Number of packages of hamburgers bought = $5
`y`

As per question statement, the second equation can be written as:

`2x+5 y = 95 ..... (2)`

Putting the value from equation (1) to equation (2):

`2x+5(x+5) = 95\\\Rightarrow 7x =95-25\\\Rightarrow x = 10`

Putting this value in the equation (1):

`y = 10+5\\\Rightarrow y =15`

Number of packages of hamburgers bought = 15

Number of packages of corndogs bought = 10