Question

Ms. Wells bought some bananas for $0.40 per pound and some oranges for $0.80 per pound. Her fruit purchase cost $8.00 and weighed 11.75 pounds. How many pounds of bananas did she buy?

A.
2.375 pounds

B.
3.50 pounds

C.
8.25 pounds

D.
9.375 pounds

Answer 1

Let \( b \) be the pounds of bananas and \( o \) be the pounds of oranges that Ms. Wells bought. We have the following two equations based on the information provided:

1. The total weight equation:
\[
b + o = 11.75
\]

2. The total cost equation:
\[
0.40b + 0.80o = 8.00
\]

We can simplify the second equation by multiplying everything by 10 to eliminate the decimals:
\[
4b + 8o = 80
\]

Now we have the system of equations:
1. \( b + o = 11.75 \)
2. \( 4b + 8o = 80 \)

From the first equation, we can express \( o \) in terms of \( b \):
\[
o = 11.75 - b
\]

Now we can substitute this expression for \( o \) into the second equation:
\[
4b + 8(11.75 - b) = 80
\]
Simplifying this, we have:
\[
4b + 94 - 8b = 80
\]
\[
-4b + 94 = 80
\]
\[
-4b = 80 - 94
\]
\[
-4b = -14
\]
\[
b = \frac{14}{4} = 3.5
\]

Thus, Ms. Wells bought \( 3.5 \) pounds of bananas.

To confirm, we can find the number of pounds of oranges as follows:
\[
o = 11.75 - 3.5 = 8.25
\]

Now, let's check the cost:
\[
\text{Cost of bananas} = 0.40 \times 3.5 = 1.4
\]
\[
\text{Cost of oranges} = 0.80 \times 8.25 = 6.6
\]
\[
\text{Total cost} = 1.4 + 6.6 = 8.00
\]

Both the total weight and the total cost match the given conditions, confirming our solution is correct.

Thus, the number of pounds of bananas that Ms. Wells bought is \( \boxed{3.50} \).