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

Let's denote the number of pounds of beans as \( b \) and the number of pounds of red lentils as \( r \). We know the following:

1. The total weight of beans and red lentils is 10 pounds: \[ b + r = 10 \]

2. The cost of beans is $2.00 per pound, so the cost of \( b \) pounds of beans is: \[ 2b \]

3. The cost of red lentils is $1.50 per pound, so the cost of \( r \) pounds of red lentils is: \[ 1.5r \]

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

Now, we can write down the system of equations:

1. \( b + r = 10 \)
2. \( 2b + 1.5r = 17 \)

Now let's solve this system of equations. From the first equation, we can express \( r \) in terms of \( b \): \[ r = 10 - b \]

Next, we can substitute \( r \) in the second equation: \[ 2b + 1.5(10 - b) = 17 \]

Now, distribute \( 1.5 \): \[ 2b + 15 - 1.5b = 17 \]

Combine like terms: \[ 0.5b + 15 = 17 \]

Subtract 15 from both sides: \[ 0.5b = 2 \]

Now, multiply both sides by 2 to solve for \( b \): \[ b = 4 \]

Now we can find \( r \) by plugging \( b \) back into the first equation: \[ r = 10 - 4 = 6 \]

So, the order contains:

• \( \boxed{4} \) pounds of beans
• \( \boxed{6} \) pounds of red lentils