Question

Liza buys three apples, a dozen bananas, and one cantaloupe for $2.36. Bob buys a dozen apples and two cantaloupe for $5.26. Carol buys two bananas and three cantaloupe for $2.77. How much do single pieces of each fruit cost?​

Answer 1

Answer:

Let the price for each fruit be denoted as follows a,b,c for apples, bananas and cantaloupes respectively.

Given:

3a+12b+1c=2.36

12a+2c=5.26

2b+3c=2.77

Solving the equation above,

2b+3c=2.77

2b=2.77-3c

b=(2.77-3c)/2

12a+2c=5.26

12a=5.26-2c

a=(5.26-2c)/12

3a+12b+c=2.36

Replacing the values of a and b per above, we now get,

[3(5.26-2c)/12]+[12(2.77-3c)/2]+c=2.36

After solving the above equation, we get the following values:

c=0.89

b=0.05

a=0.29

Hence the price of each apple = $0.29, banana = $0.05, cantaloupe = $0.89