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A grocery bag contains x apples, each weighing One-third of a pound, and y pounds of grapes. The total weight of the grocery bag is less than 5 pounds. Which graph represents the possible numbers of apples and pounds of grapes that can be in the bag? 1. A graph titled Grocery Bag Contents shows number of apples on the x-axis, from 0 to 18, and Pounds of Grapes on the y-axis, from 0 to 10. A dashed straight line has a negative slope and goes through (0, 5) and (15, 0). Everything above the line is shaded. 2. A graph titled Grocery Bag Contents shows number of apples on the x-axis, from 0 to 18, and Pounds of Grapes on the y-axis, from 0 to 10. A dashed straight line has a negative slope and goes through (0, 5) and (15, 0). Everything below and to the left of the line is shaded. 3. A graph titled Grocery Bag Contents shows number of apples on the x-axis, from 0 to 10, and Pounds of Grapes on the y-axis, from 0 to 18. A dashed straight line has a negative slope and goes through (0, 15) and (5, 0). Everything to the right of the line is shaded. 4. A graph titled Grocery Bag Contents shows number of apples on the x-axis, from 0 to 10, and Pounds of Grapes on the y-axis, from 0 to 18. A dashed straight line has a negative slope and goes through (0, 15) and (5, 0). Everything to the left of the line is shaded.

3. Turkey sandwiches cost $2.50 and veggie wraps cost $3.50 at a snack stand. Ben has sold no more than $30 worth of turkey sandwiches and veggie wraps in the first hour of business. Let x represent the number of turkey sandwiches and y represent the number of veggie wraps. The inequality 2.50x+3.50y30 represents the food sales in the first hour.

If Ben has sold 4 veggie wraps, what is the maximum number of turkey sandwiches Ben could have sold?

5
6
7
10

4. It takes Dimitri 9 minutes to make a simple bracelet and 20 minutes to make a deluxe bracelet. He has been making bracelets for longer than 120 minutes. If x represents the number of simple bracelets that he has made and y represents the number of deluxe bracelets he has made, the inequality 9x + 20y > 120 represents the scenario.

Which is a possible combination of bracelets that Dimitri may have made?

3 simple bracelets and 4 deluxe bracelets
0 simple bracelets and 6 deluxe bracelets
12 simple bracelets and 0 deluxe bracelets
7 simple bracelets and 3 deluxe bracelets

6. Mr. Ishimoto ordered x new math books and y new workbooks for his class. The total weight of the box of books cannot be more than 50 pounds. If each math book weighs 3.2 pounds and each workbook weighs 0.8 pounds, which inequality represents the maximum number of each type of book that can be shipped in a single box?

3.2x + 0.8y < 50
3.2x + 0.8y ≤ 50
0.8x + 3.2y < 50
0.8x + 3.2y ≤ 50

7. Dominick is training for a race. He spends 0.75 hours running each time he runs and 1.5 hours swimming each time he swims. This week, he spent more than 6 hours training for the race. Which graph represents his possible training times this week? 1. A graph titled Dominick apostrophe s Training shows number of runs on the x-axis, from 0 to 10, and number of swims on the y-axis, from 0 to 5. A dashed straight line with a negative slope goes through (0, 4) and (8, 0). Everything to the right of the line is shaded. 2. A graph titled Dominick apostrophe s Training shows number of runs on the x-axis, from 0 to 10, and number of swims on the y-axis, from 0 to 5. A dashed straight line with a negative slope goes through (0, 4) and (8, 0). Everything to the left of the line is shaded. 3. A graph titled Dominick apostrophe s Training shows number of runs on the x-axis, from 0 to 5, and number of swims on the y-axis, from 0 to 10. A dashed straight line with a negative slope goes through (0, 8) and (4, 0). Everything to the right of the line is shaded. 4. A graph titled Dominick apostrophe s Training shows number of runs on the x-axis, from 0 to 5, and number of swims on the y-axis, from 0 to 10. A dashed straight line with a negative slope goes through (0, 8) and (4, 0). Everything to the left of the line is shaded.

8. A hook in an office storage closet can hold no more than 6 pounds. An order of jumbo paperclips weighs 2 pounds and an order of packing tape weighs 3 pounds. If x is the number of orders of paperclips and y is the number of orders of packing tape, which graph represents the overall equation represented by this scenario (all points may not apply to the scenario)? 1. On a coordinate plane, a solid straight line has a negative slope and goes through (0, 2) and (3, 0). Everything below and to the left of the line is shaded. 2. On a coordinate plane, a solid straight line has a negative slope and goes through (0, 2) and (3, 0). Everything above and to the right of the line is shaded. 3. On a coordinate plane, a solid straight line has a negative slope and goes through (0, 3) and (2, 0). Everything to the right of the line is shaded. 4. On a coordinate plane, a solid straight line has a negative slope and goes through (0, 3) and (2, 0). Everything to the left of the line is shaded.

9. Last year, Jess saw x dramas and y comedies at the movie theater. If she went to the theater no more than 8 times, which inequality best represents the number of movies she saw?

x + y < 8
x + y > 8
x + y ≤ 8
x + y ≥ 8

10. Dan bought x pounds of potatoes for $0.85 per pound and y pounds of grapes for $1.29 per pound. The total cost was less than $5. Which inequality represents his purchase?

1.29x + 0.85y < 5
1.29x + 0.85y > 5
0.85x + 1.29y > 5
0.85x + 1.29y < 5

3 answers

Here are the answers to the provided questions:

  1. Grocery Bag Weights: The total weight of the grocery bag is \( \frac{1}{3}x + y < 5 \). To represent this graphically, we first rearrange it into slope-intercept form. From \( y < 5 - \frac{1}{3}x \), we can identify that the line has a negative slope and intersects the y-axis at 5 and x-axis at 15. The shaded area must be above this line since we want to represent weights less than 5 pounds. Therefore, Option 1 represents the solution correctly.

  2. Maximum Number of Turkey Sandwiches: If Ben sells 4 veggie wraps, the equation becomes: \[ 2.50x + 3.50(4) \leq 30 \] \[ 2.50x + 14 \leq 30 \] \[ 2.50x \leq 16 \Rightarrow x \leq \frac{16}{2.5} = 6.4 \] Therefore, the maximum number of turkey sandwiches Ben could have sold is 6.

  3. Combinations of Bracelets: The inequality \( 9x + 20y > 120 \) checks the combinations. Testing:

    • \( 3 \) simple and \( 4 \) deluxe: \( 9(3) + 20(4) = 27 + 80 = 107\) (not possible)
    • \( 0 \) simple and \( 6 \) deluxe: \( 9(0) + 20(6) = 0 + 120 = 120\) (not possible)
    • \( 12 \) simple and \( 0 \) deluxe: \( 9(12) + 20(0) = 108 + 0 = 108\) (not possible)
    • \( 7 \) simple and \( 3 \) deluxe: \( 9(7) + 20(3) = 63 + 60 = 123\) (possible) Thus, 7 simple bracelets and 3 deluxe bracelets is a valid combination.

  4. Weight of Books: The total weight constraint is given by \( 3.2x + 0.8y \leq 50 \). Therefore, the correct inequality that represents the maximum number of books is 3.2x + 0.8y ≤ 50.

  5. Dominick's Training: For the training, the inequality is \( 0.75x + 1.5y > 6 \). Transforming leads us to the line \( 0.75x + 1.5y = 6 \) (which simplifies to \( x + 2y = 8 \)). Thus, the graph should show the region above this line. Therefore, Option 1 is correct, as it shades to the right of the line.

  6. Hook Capacity: The orders of paperclips and packing tape must satisfy; \( 2x + 3y \leq 6 \). The line will cross the y-axis at \( 2 \) (when \( x = 0 \)) and x-axis at \( 3 \) (when \( y = 0 \)). Hence, since we are considering the total weights below or to the left of the line, the correct option is Option 1.

  7. Movies Seen: Since the maximum number of times Jess saw movies is 8, then the correct inequality representing this is \( x + y \leq 8 \). Thus the answer is x + y ≤ 8.

  8. Cost of Potatoes and Grapes: The cost inequality representing his purchases would be \( 0.85x + 1.29y < 5 \). This captures the total cost limitation. Therefore, the answer is 0.85x + 1.29y < 5.

These are the solutions to the provided questions. If there are more specific explanations needed for any of the steps, feel free to ask!

i skipped 1 and 5 but
1. Lola bought x pencils that cost $0.25 each and y erasers that cost $0.50. She spent less than $3. Which graph represents Lola’s purchase?
A graph titled Lola apostrophe s Purchase shows number of pencils on the x-axis, from 0 to 20, and number of erasers on the y-axis, from 0 to 10. A dashed straight line has a negative slope and goes through (0, 6) and (12, 0). Everything to the left of the line is shaded.

2. A grocery bag contains x apples, each weighing 1/3 of a pound, and y pounds of grapes. The total weight of the grocery bag is less than 5 pounds. Which graph represents the possible numbers of apples and pounds of grapes that can be in the bag?
A graph titled Grocery Bag Contents shows number of apples on the x-axis, from 0 to 18, and Pounds of Grapes on the y-axis, from 0 to 10. A dashed straight line has a negative slope and goes through (0, 5) and (15, 0). Everything below and to the left of the line is shaded.

5. One company estimates same-day delivery as more than three less than half the total number of miles. Which graph represents the overall equation represented by this scenario (all points may not apply to the scenario)? Note that the graphs have miles for the independent variable on the x-axis, and the y-axis is a unit of time dependent on the number of miles.
okay the graph witht the most shaded but colored on the top and the line going more higher is right

Let's break down the scenarios you skipped and confirm the correct answers for each of them:

1. Lola's Purchase

Lola bought \(x\) pencils at $0.25 each and \(y\) erasers at $0.50 each, spending less than $3. We can write the inequality for her expenses as:

\[ 0.25x + 0.50y < 3 \]

To simplify, we can multiply through by 4 to eliminate decimals:

\[ x + 2y < 12 \]

To express this as an equation for graphing, we'd rearrange it to form a line:

\[ 2y < 12 - x \quad \Rightarrow \quad y < 6 - 0.5x \]

Interpretation of the Graph

The line \(y = 6 - 0.5x\) intersects the y-axis at \(y = 6\) (when \(x = 0\)) and the x-axis at \(x = 12\) (when \(y = 0\)).

  • The line has a negative slope, and we want the region below this line since she spent less than $3.

Looking at your provided graph description, the dashed line goes through points (0, 6) and (12, 0) and shades everything to the left, which is incorrect per our inequality requirement.

However, if this shading and line truly represent the described inequality, it looks like you may have misinterpreted the shaded area and inequality sign. The correct representation should shade below the line instead of to the left, based on $0.25x + 0.50y < 3$.

Conclusion for Lola's Purchase

Given your description and the demand for shading below the line instead of to the left, the graphical representation for this indicates that the provided graph does not represent Lola’s purchase correctly.

2. Grocery Bag Contents

This inequality is given by \( \frac{1}{3}x + y < 5 \), which rearranges to present in linear form:

\[ y < 5 - \frac{1}{3}x \]

The intercepts of the line are:

  • y-intercept = 5 (when \(x = 0\))
  • x-intercept = 15 (when \(y = 0\))

Interpretation of the Graph

For this inequality, we want the shaded area below the line, which represents the total weight of the grocery bag being less than 5 pounds.

Your description of the graph goes through points (0, 5) and (15, 0) and shades everything below it. This agrees with our inequality since we want weights less than 5.

Conclusion for Grocery Bag Contents

The graph as you described seems correct, so this graph does represent the possible numbers of apples and pounds of grapes in the bag.

5. Delivery Time Estimate

The statement "one company estimates same-day delivery as more than three less than half the total number of miles" can be expressed as:

\[ y > \frac{1}{2}x - 3 \]

This implies:

  • The line has a slope of 0.5 (which means it rises as the number of miles increases), and it crosses the y-axis at \( -3 \).

Graph Representation

We are looking for a line where the area above the line is shaded because we're interested in times that are greater than the estimated delivery time.

  • A graph with the most shaded areas above the line with a slope moving upward reflecting the given condition would be the correct choice.

Conclusion for Delivery Estimate

Your indication that the graph with the most shading above the line and moving higher aligns with the overall condition of delivery time being "more than" suggests it is correctly represented in the graph.

If you have any further doubts or need clarifications, feel free to ask!