Question

Several customers order small fruit baskets filled with apples, bananas, and oranges. Let a represent the price per pound of apples, b represent the price per pound of bananas, and c represent the price per pound of oranges. The system represents the number of pounds of each type of fruit and the total price of each fruit basket. How much per pound does each type of fruit cost? apples: $2. 00/lb, bananas: $0. 50/lb, and oranges: $3. 00 apples: $2. 00, bananas: $1. 50/lb, and oranges: $3. 00/lb apples: $2. 50/lb, bananas $0. 25/lb, and oranges: $3. 00/lb apples: $2. 50, bananas: $0. 75, oranges: 3. 00/lb.

Answer 1

Apples costs $2/pound, oranges costs $0.5/pound and bananas costs $3/pound

Given the following parameters:

• a represent the price per pound of apples

• b represent the price per pound of bananas

• c represent the price per pound of oranges

Solving the equation simultaneously;

a+2b+3c=12 .......................... 1

3a+2b+5c=22 ....................... 2

2a+4b+4c=18 ......................... 3

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Subtravt equation 1 from 2 to have;

(a-3a)+(3c-5c) = 12-22

-2a - 2c = -10

a + c = 5 ....................... 4

From equation 2 and 3;

3a+2b+5c=22 ....................... 2 * 2

2a+4b+4c=18 ......................... 3 * 1

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6a+4b+10c=44  

2a+4b+4c=18

Subtract both expressions

4a + 6c = 26

2a + 3c = 13 ........................... 5

Solve equation 4 and 5 simultaneously;

a + c = 5 ....................... 4

2a + 3c = 13 ........................... 5

From equation 4, a = 5-c

Substitute a = 5 - c into equation 5;

2(5-c) + 3c = 13

10-2c + 3c = 13

10 + c = 13

c = 13 - 10

c = 3

Substitute c = 3 into equation 4

a + c = 5

a = 5 - c

a = 5 - 3

a = 2

Substitute a = 2 and c = 3 into equation 1:

a+2b+3c=12

2 + 2b + 3(3) = 12

2b + 11 = 12

2b = 12 - 11

2b = 1

b = 0.5

This shows that apples costs $2/pound, oranges costs $0.5/pound and bananas costs $3/pound

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