Question

At the county fair, Darius can purchase 3 candy apples and 4 bags of peanuts for $11.33. He can purchase 9 candy apples and 5 bags of peanuts for $23.56. Darius decides to purchase 2 candy apples and 3 bags of peanuts.
What is the total cost of his purchase?

Answer 1

Let c represents the cost of a candy apple and b represents the cost of a bag of peanuts.

Darius can purchase 3 candy apples and 4 bags of peanuts. So his total cost would be 3c + 4b. Darius can buy 3 candy apples and 4 bags of peanuts in $11.33,so we can write the equation as: 

3c + 4b = 11.33   (1)

Darius can purchase 9 candy apples and 5 bags of peanuts. So his total cost would be 9c + 5b. Darius can buy 9 candy apples and 5 bags of peanuts in $23.56,so we can write the equation as: 

9c + 5b = 23.56   (2)

Darius decides to purchase 2 candy apples and 3 bags of peanuts. The total cost in this case will be 2c + 3b. To find this first we need to find the cost of each candy apple and bag of peanuts by solving the above two equations.

Multiplying equation 1 by three and subtracting equation 2 from it, we get:

3(3c + 4b) - (9c + 5b) = 3(11.33) - 23.56

9c + 12b - 9c - 5b = 10.43

7b = 10.43

b = $1.49

Using the value of b in equation 1, we get:

3c + 4(1.49) = 11.33

3c = 5.37

c = $ 1.79

Thus, cost of one candy apple is $1.79 and cost of one bag of peanuts is $1.49.

So, 2c + 3b = 2(1.79) + 3(1.49) = $ 8.05

Therefore, Darius can buy 2 candy apples and 3 bags of peanuts in $8.05