Question

11/14
At a farmer's market the total cost of 3 pounds of red apples and 4 pounds of green apples is $8, including tax. The total cost of 6 pounds of red apples and 1 pound of green apples is $6.20, including tax. What is the price per pound of the green apples?
$2.20
$1.40
$3.00
$0.80

Answer 1

Let's denote the price per pound of red apples as \( r \) and the price per pound of green apples as \( g \). We can create a system of equations based on the information given:

1. From the first scenario:
\[
3r + 4g = 8
\]

2. From the second scenario:
\[
6r + 1g = 6.20
\]

Now we have the system of equations:
1. \( 3r + 4g = 8 \) (Equation 1)
2. \( 6r + g = 6.20 \) (Equation 2)

We can solve this system of equations.

First, let's solve Equation 2 for \( g \):
\[
g = 6.20 - 6r
\]

Now, substitute this expression of \( g \) into Equation 1:
\[
3r + 4(6.20 - 6r) = 8
\]

Distributing the 4:
\[
3r + 24.8 - 24r = 8
\]

Combining like terms (the \( r \) terms):
\[
-21r + 24.8 = 8
\]

Subtract 24.8 from both sides:
\[
-21r = 8 - 24.8
\]
\[
-21r = -16.8
\]

Now divide by -21:
\[
r = \frac{16.8}{21} = 0.8
\]

Now that we know \( r \), we can substitute it back into the equation for \( g \):
\[
g = 6.20 - 6(0.8)
\]
\[
g = 6.20 - 4.8
\]
\[
g = 1.40
\]

Thus, the price per pound of green apples is \( \boxed{1.40} \).