An order of beans and red lentils weighs 10 pounds and costs $17.

Question

Beans: $2.00 per pound
Red lentils: $1.50 per pound
How many pounds of beans and red lentils are in this order?
Start by writing an expression to represent the cost of b pounds of beans. Keep in mind that 1 pound of beans costs $2.00
Cost of b
pounds of
beans
+
Cost of r pounds of red lentils
=
Total Cost
+
?

Answer 1

To solve the problem, let's define our variables based on the information provided:

• Let \( b \) be the number of pounds of beans.
• Let \( r \) be the number of pounds of red lentils.

From the problem, we have two key pieces of information:

1. The total weight of the order is 10 pounds: \[ b + r = 10 \]

2. The total cost of the order is $17: \[ 2b + 1.5r = 17 \]

Now, we need to write an expression to represent the costs.

1. Cost of \( b \) pounds of beans: Since the cost of beans is $2.00 per pound, we can express this as: \[ \text{Cost of } b \text{ pounds of beans} = 2b \]

2. Cost of \( r \) pounds of red lentils: Since the cost of red lentils is $1.50 per pound, we can express this as: \[ \text{Cost of } r \text{ pounds of red lentils} = 1.5r \]

3. Total Cost: The total cost of the order, as given, is $17: \[ \text{Total Cost} = 2b + 1.5r = 17 \]

So, we have the following expressions:

\[ 2b + 1.5r = 17 \]

Now, we can substitute \( r \) from the first equation into the second equation:

From the first equation: \[ r = 10 - b \]

Substituting \( r \) into the total cost equation: \[ 2b + 1.5(10 - b) = 17 \] \[ 2b + 15 - 1.5b = 17 \] \[ 0.5b + 15 = 17 \] \[ 0.5b = 2 \] \[ b = 4 \]

Now, substituting \( b = 4 \) back into the first equation to find \( r \): \[ 4 + r = 10 \] \[ r = 6 \]

Thus, the solution is:

• Pounds of beans: \( 4 \) pounds
• Pounds of red lentils: \( 6 \) pounds

Final Answer:

• Beans: 4 pounds
• Red lentils: 6 pounds