A small fruit basket with 6 apples and 6 oranges costs $7.50. A different fruit basket with 10 apples and 5 oranges costs $8.75. If x is the cost of one apple and y is the cost of one orange, the system of equations below can be used to determine the cost of one apple and one orange.

Question

6x+6y=7.50

10x+5y=8.75

What is the cost of one apple?

0.25
0.5
0.75
1.00

Answer 1

To solve for the cost of one apple (x) and one orange (y), we have the following system of equations:

1. \( 6x + 6y = 7.50 \)
2. \( 10x + 5y = 8.75 \)

Let's simplify the first equation by dividing all terms by 6:

\[ x + y = 1.25 \quad \text{(Equation 1)} \]

Now, simplify the second equation by dividing all terms by 5:

\[ 2x + y = 1.75 \quad \text{(Equation 2)} \]

Now we can solve the system of equations. We can substitute Equation 1 into Equation 2. From Equation 1, we can express \(y\) in terms of \(x\):

\[ y = 1.25 - x \]

Now substitute this expression for \(y\) into Equation 2:

\[ 2x + (1.25 - x) = 1.75 \]

Combine like terms:

\[ 2x - x + 1.25 = 1.75 \] \[ x + 1.25 = 1.75 \]

Now, solve for \(x\):

\[ x = 1.75 - 1.25 \] \[ x = 0.50 \]

Thus, the cost of one apple is \($0.50\).

So the answer is:

0.5