Question

Three apples and four bananas cost $4.85. Three apples and ten bananas cost $8.75. Find the cost of an apple.

use x for apples and y for bananas for your variables

a
x = 1.26 y = 2.30

b
x = 0.75 y = 0.65

c
x= 0.95 y = 1.10

Answer 1

Let's set up the equations based on the information given. Let \( x \) be the cost of an apple and \( y \) be the cost of a banana.

From the problem, we have the following equations:

1. \( 3x + 4y = 4.85 \) \quad (Equation 1)
2. \( 3x + 10y = 8.75 \) \quad (Equation 2)

Next, we can solve these equations.

### Step 1: Eliminate \( x \)

Subtract Equation 1 from Equation 2:

\[
(3x + 10y) - (3x + 4y) = 8.75 - 4.85
\]

This simplifies to:

\[
6y = 3.90
\]

### Step 2: Solve for \( y \)

Now, divide both sides by 6:

\[
y = \frac{3.90}{6} = 0.65
\]

### Step 3: Substitute \( y \) back to find \( x \)

Now that we have \( y \), substitute \( y = 0.65 \) back into Equation 1:

\[
3x + 4(0.65) = 4.85
\]

This simplifies to:

\[
3x + 2.60 = 4.85
\]

Now, subtract 2.60 from both sides:

\[
3x = 4.85 - 2.60
\]
\[
3x = 2.25
\]

Now, divide by 3:

\[
x = \frac{2.25}{3} = 0.75
\]

### Conclusion

The cost of an apple is \( x = 0.75 \) and the cost of a banana is \( y = 0.65 \).

Thus, the answer is:

**b** \( x = 0.75, y = 0.65 \)