Question

A farmer is distributing two types of produce: apples (x) and oranges (y). Each box of apples is sold for $3, and each box of oranges is sold for $2. On a certain day, the farmer sold a total of 80 boxes of produce and made $190 from these sales.

Select TWO that apply.

A.
Total sales amount: 3x + 2y = 190
B.
Number of boxes sold: x + y = 190
C.
There were 30 apples sold.
D.
There were 55 oranges sold.
E.
Total sales amount: 3y + 2x = 190

Answer 1

To analyze the problem, we have two equations based on the information provided:

1. The farmer sold a total of 80 boxes of produce, which gives us the equation:
\[
x + y = 80
\]

2. The total amount made from the sales is $190, leading to the equation:
\[
3x + 2y = 190
\]

Now, let's assess the options given:

A. **Total sales amount: 3x + 2y = 190** - This is correct because it accurately represents the total sales amount equation derived from the selling prices of apples and oranges.

B. **Number of boxes sold: x + y = 190** - This is incorrect. The total number of boxes sold is 80, not 190.

C. **There were 30 apples sold.** - We will determine if this is true later.

D. **There were 55 oranges sold.** - We will determine if this is true later.

E. **Total sales amount: 3y + 2x = 190** - This is incorrect. The form is not aligned with the prices of the produce.

Now, let's solve the equations to check the conditions in options C and D:

From the first equation, \( x + y = 80 \):
\[
y = 80 - x
\]

Substituting \( y \) in the second equation:
\[
3x + 2(80 - x) = 190
\]
Expanding this:
\[
3x + 160 - 2x = 190
\]
Simplifying:
\[
x + 160 = 190
\]
\[
x = 190 - 160 = 30
\]

Now substituting \( x = 30 \) back into the first equation to find \( y \):
\[
30 + y = 80
\]
\[
y = 80 - 30 = 50
\]

So, from our calculations:
- The number of apples sold (x) is 30.
- The number of oranges sold (y) is 50.

Now evaluating options C and D:
- C (There were 30 apples sold): This is **true**.
- D (There were 55 oranges sold): This is **false**; there were 50 oranges sold.

Thus, the correct answers are:
- **A. Total sales amount: 3x + 2y = 190**
- **C. There were 30 apples sold.**