Question

Three customers buy fruit in the same grocery store.

Customer 1 buys 3 apples, 2 oranges, 1 pear for $8.50
Customer 2 buys 2 apples, 1 orange, 2 pears for $7.50
Customer 3 buys 1 apple, 2 oranges, 3 pears for $9.50
Solve the system of equations to determine the cost of each apple, orange, and pear.
O: A apples $1.75, oranges $1.50, pears $1.25

Answer 1

To solve the system of equations, substitute the values of one variable into the other equations and solve for the remaining variables. The cost of each apple, orange, and pear is: Apples = $-4.50, Oranges = $7.25, Pears = $2.50.

Step-by-step explanation:

We can solve the system of equations to determine the cost of each apple, orange, and pear. Let's assign variables to the cost of each fruit: Apples = A, Oranges = O, Pears = P.

From the given information, we can set up the following equations:

3A + 2O + P = 8.50

2A + O + 2P = 7.50

A + 2O + 3P = 9.50

Multiplying the second equation by 2, we get:

4A + 2O + 4P = 15.00

Subtracting the first equation from the new equation, we have:

A + 3P = 6.50

Subtracting the third equation from the second equation, we have:

A + P = -2.00

Substituting the value of A from the second equation into the first equation, we get:

(-2.00) + 3P = 6.50

Solving this equation, we find:

P = 2.50

Substituting the value of P into the second equation, we can find the cost of A:

A + 2.50 = -2.00

Solving for A, we find:

A = -4.50

Finally, substituting the values of A and P into the third equation, we can find the cost of O:

(-4.50) + 2O + (2.50 * 3) = 9.50

Simplifying this equation, we find:

2O = 14.50

O = 7.25

Therefore, the cost of each apple, orange, and pear is: Apples = $-4.50, Oranges = $7.25, Pears = $2.50.