Question

KARUNA OPENED A CANDY SHOP AND SELLS CHOCOLATE AND PEANUT

BUTTER FUDGE BY THE POUND. THE CHOCOLATE FUDGE COSTS $3.20 PER
POUND AND THE PEANUT BUTTER FUDGE COSTS $3.00 PER POUND. ON A
GIVEN DAY KARUNA'S CANDY SHOP SELLS 15.5 POUNDS OF FUDGE FOR A
GROSS PROFIT OF $48.50
A WRITE A SYSTEM OF EQUATIONS TO DESCRIBE THE SCENARIO WHERE C
REPRESENTS THE NUMBER OF POUNDS OF CHOCOLATE FUDGE SOLD,
AND P REPRESENTS THE NUMBER OF POUNDS OF PEANUT BUTTER
FUDGE SOLD
B. HOW MANY POUNDS OF PEANUT BUTTER FUDGE DID KARUNA'S CANDY
SHOP SELL?

Answer 1

A. System of equations:

`3.2C+3P=48.5\\C+P=15.5`

B. 5.5 pounds of peanut butter fudge were sold.

Explanation:

Given:

Cost of chocolate fudge = $3.20

Cost of peanut butter fudge = $3.00

Total pounds sold = 15.5

Total gross profit = $48.50

C is the number of pounds of chocolate fudge sold.

P is the number of pounds of peanut butter fudge sold.

To find:

System of equations and number of pounds of peanut butter fudge sold = ?

Solution:

As per given conditions:

1.
`C+P=15.5`

Gross profit from Chocolate fudge:
`3.20 * C`

Gross profit from Peanut Butter fudge:
`3.00 * P`

Total gross profit =
`3.20C+3.00P = 48.50`

So, the system of equations is:

`3.2C+3P=48.5\\C+P=15.5`

2. To find P.

Let us solve the equations.

Multiply 2nd equation with 3 and subtracting from 1st equation:

`0.2C = 48.5- 3 * 15.5\\\Rightarrow 0.2C = 48.5- 46.5\\\Rightarrow C = 10\ pounds`

Putting in 2nd equation:

`10+P=15.5\\\Rightarrow P =5.5\ pounds`

So, the answer is:

5.5 pounds of peanut butter fudge were sold.