Let's denote the price per pound of apples as $ A $ and the price per pound of blueberries as $ B $.

From the information given, we can set up the following system of equations based on the sales and revenue:

1. $ 20A + 50B = $160 $ (Equation 1)
2. $ 38A + 10B = $134 $ (Equation 2)

We will solve this system of equations step by step.

**Step 1: Simplify Equation 1**

Divide Equation 1 by 10 to make the coefficients smaller:
$$ 2A + 5B = 16 $$ (Equation 3)

**Step 2: Simplify Equation 2**

Divide Equation 2 by 2 to make the coefficients smaller:
$$ 19A + 5B = 67 $$ (Equation 4)

**Step 3: Eliminate one variable**

Subtract Equation 3 from Equation 4 to eliminate $ B $:
$$ (19A + 5B) - (2A + 5B) = 67 - 16 $$
$$ 17A = 51 $$
$$ A = 3 $$

**Step 4: Substitute $ A $ back into one of the original equations**

Substitute $ A = 3 $ into Equation 3:
$$ 2(3) + 5B = 16 $$
$$ 6 + 5B = 16 $$
$$ 5B = 10 $$
$$ B = 2 $$

**Step 5: Verify the solution**

Substitute $ A = 3 $ and $ B = 2 $ back into the original equations to ensure they are correct.

For Equation 1:
$$ 20(3) + 50(2) = 60 + 100 = 160 $$ (Correct)

For Equation 2:
$$ 38(3) + 10(2) = 114 + 20 = 134 $$ (Correct)

Therefore, the price per pound of apples is $ \$3 $ and the price per pound of blueberries is $ \$2 $.

Question

Let's denote the price per pound of apples as $ A $ and the price per pound of blueberries as $ B $.

From the information given, we can set up the following system of equations based on the sales and revenue:

1. $ 20A + 50B = $160 $  (Equation 1)
2. $ 38A + 10B = $134 $  (Equation 2)

We will solve this system of equations step by step.

**Step 1: Simplify Equation 1**

Divide Equation 1 by 10 to make the coefficients smaller:
$$ 2A + 5B = 16 $$  (Equation 3)

**Step 2: Simplify Equation 2**

Divide Equation 2 by 2 to make the coefficients smaller:
$$ 19A + 5B = 67 $$  (Equation 4)

**Step 3: Eliminate one variable**

Subtract Equation 3 from Equation 4 to eliminate $ B $:
$$ (19A + 5B) - (2A + 5B) = 67 - 16 $$
$$ 17A = 51 $$
$$ A = 3 $$

**Step 4: Substitute $ A $ back into one of the original equations**

Substitute $ A = 3 $ into Equation 3:
$$ 2(3) + 5B = 16 $$
$$ 6 + 5B = 16 $$
$$ 5B = 10 $$
$$ B = 2 $$

**Step 5: Verify the solution**

Substitute $ A = 3 $ and $ B = 2 $ back into the original equations to ensure they are correct.

For Equation 1:
$$ 20(3) + 50(2) = 60 + 100 = 160 $$  (Correct)

For Equation 2:
$$ 38(3) + 10(2) = 114 + 20 = 134 $$  (Correct)

Therefore, the price per pound of apples is $ \$3 $ and the price per pound of blueberries is $ \$2 $.

Knowee AI · Accepted Answer