Question

At the local harvest festival Marty bought 2 pumpkin pie slices and 2 cups of hot chocolate $10.00. Patty bought 4 slices of pie and 5 cups of hot chocolate for $22.50. How much is a slice of pumpkin pie and how much is a cup of hot chocolate?

Answer 1

1 cup of hot chocolate is $2.5

1 slice of pumpkin pie is $2.5

Explanation:

Represent Pumpkin Pie with P and Hot Chocolate with C:

Marty:

`2P + 2H = 10`

Patty:

`4P + 5H = 22.5`

So, we have the following set of equation:

`2P + 2H = 10` -------- (1)

`4P + 5H = 22.5` -------- (2)

Multiply the first equation by 2

`2(2P + 2H = 10)`

`4P + 4H = 20` -------- (3)

Subtract (3) from (2)

`4P + 5H = 22.5`

`4P + 4H = 20`

--------------------------

`5H - 4H = 22.5 - 20`

`H = 2.5`

Substitute 2.5 for H in
`2P + 2H = 10`

`2P + 2 * 2.5 = 10`

`2P + 5 = 10`

`2P = 10 - 5`

`2P = 5`

Divide through by 2

`P = (5)/(2)`

`P=2.5`

Hence, 1 cup of hot chocolate is $2.5 and 1 slice of pumpkin pie is $2.5