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

Answer:

1 cup of hot chocolate is $2.5

1 slice of pumpkin pie is $2.5

Step-by-step 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

$P = \frac{5}{2}$

$P=2.5$

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