Question

Dalton sells popcorn for $4 a bag and cans of juice for $1.25 a can. Today, his goal is to sell $500 worth of popcorn and juice.
Write an equation that represents the problem in standard form. Let x represent the number of bags of popcorn Dalton sells and let y represent the number of cans of juice he sells.

__x + __y = __

Answer 1

4x + 1.25y = 500
Choose the correct response from the drop-down menu.

The x-intercept is ___.
A. 1.25
B. 4
C. 125
D. 400
The y-intercept is ___.
A. 1.25
B. 4
C. 125
D. 400

Answer 2

Enter your responses in the boxes.

The x-intercept means that Dalton can make his goal by selling ___ bags of popcorn and ___ cans of juice.

The y-intercept means that Dalton can make his goal by selling ___ bags of popcorn and ___ cans of juice.

Answer 3

To write an equation that represents the problem, we can express the relationships between the sales of popcorn and juice.

Let:
- \( x \) be the number of bags of popcorn sold, where each bag of popcorn sells for $4. Therefore, the total revenue from popcorn sold is \( 4x \).
- \( y \) be the number of cans of juice sold, where each can of juice sells for $1.25. Therefore, the total revenue from juice sold is \( 1.25y \).

Dalton's goal is to achieve a total sales revenue of $500. We can set up the equation as follows:

\[
4x + 1.25y = 500
\]

To convert this equation into standard form \( Ax + By = C \), we can eliminate the decimal by multiplying the entire equation by 4 (the least common multiple of the denominators):

\[
4(4x) + 4(1.25y) = 4(500)
\]
\[
16x + 5y = 2000
\]

Now, we can fill in the blanks for the standard form:

- The coefficient for \( x \) is 16.
- The coefficient for \( y \) is 5.
- The constant term on the right side of the equation is 2000.

Thus, the equation in standard form is:

\[
16x + 5y = 2000
\]

So, the completed equation is:

__16__x + __5__y = __2000__

Answer 4

To find the x-intercept and y-intercept of the equation \(4x + 1.25y = 500\), we will follow these steps:

### Finding the x-intercept:
To find the x-intercept, set \(y = 0\) and solve for \(x\):

\[
4x + 1.25(0) = 500
\]
\[
4x = 500
\]
\[
x = \frac{500}{4} = 125
\]

So, the x-intercept is **125**.

### Finding the y-intercept:
To find the y-intercept, set \(x = 0\) and solve for \(y\):

\[
4(0) + 1.25y = 500
\]
\[
1.25y = 500
\]
\[
y = \frac{500}{1.25} = 400
\]

So, the y-intercept is **400**.

### Summary:
- The x-intercept is **C. 125**.
- The y-intercept is **D. 400**.

Answer 5

To interpret the x-intercept and y-intercept in the context of Dalton's sales of popcorn and juice:

### X-intercept:
The x-intercept is when \( y = 0 \). From our previous calculation, we found that the x-intercept is 125. This means that if Dalton sells 125 bags of popcorn and no cans of juice, he will reach his goal of $500.

So, for the **x-intercept**:
- Dalton can make his goal by selling **125** bags of popcorn and **0** cans of juice.

### Y-intercept:
The y-intercept is when \( x = 0 \). From our previous calculation, we determined that the y-intercept is 400. This means that if Dalton sells no bags of popcorn and 400 cans of juice, he will reach his goal of $500.

So, for the **y-intercept**:
- Dalton can make his goal by selling **0** bags of popcorn and **400** cans of juice.

### Responses:
The x-intercept means that Dalton can make his goal by selling **125** bags of popcorn and **0** cans of juice.

The y-intercept means that Dalton can make his goal by selling **0** bags of popcorn and **400** cans of juice.