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.

Question

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

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 2

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 3

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 4

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 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.