Questions: The 8th graders are selling chips and candy to collect money for their end-of-the year dance. They would like to raise at least 425. They estimate that they will sell at most 65 items a day. They will earn 0.50 for each bag of chips sold and 0.75 for each bag of candy sold. Let x represent the total bags of chips sold and y the total bags of candy. Write a system of linear inequalities to represent the number of days it will take to reach their goal. A. 0.50 x+0.75 y ≤ 425 x+y ≤ 65 B. 0.50 x+0.75 y<425 x+y<65 C. 0.50 x+0.75 y ≥ 425 x+y ≤ 65 D. 0.50 x+0.75 y>425 x+y ≤ 65

The 8th graders are selling chips and candy to collect money for their end-of-the year dance. They would like to raise at least 425. They estimate that they will sell at most 65 items a day. They will earn 0.50 for each bag of chips sold and 0.75 for each bag of candy sold. Let x represent the total bags of chips sold and y the total bags of candy. Write a system of linear inequalities to represent the number of days it will take to reach their goal.

A. 0.50 x+0.75 y ≤ 425
x+y ≤ 65

B. 0.50 x+0.75 y<425
x+y<65

C. 0.50 x+0.75 y ≥ 425
x+y ≤ 65

D. 0.50 x+0.75 y>425
x+y ≤ 65
Transcript text: The 8th graders are selling chips and candy to collect money for their end-of-the year dance. They would like to raise at least $\$ 425$. They estimate that they will sell at most 65 items a day. They will earn $\$ 0.50$ for each bag of chips sold and $\$ 0.75$ for each bag of candy sold. Let x represent the total bags of chips sold and y the total bags of candy. Write a system of linear inequalities to represent the number of days it will take to reach their goal. \[ \begin{array}{l} \text { A. } 0.50 x+0.75 y \leq 425 \\ x+y \leq 65 \end{array} \] \[ \begin{array}{l} \text { B. } 0.50 x+0.75 y<425 \\ x+y<65 \end{array} \] \[ \begin{array}{l} \text { C. } 0.50 x+0.75 y \geq 425 \\ x+y \leq 65 \end{array} \] \[ \text { D. } 0.50 x+0.75 y>425 \] \[ x+y \leq 65 \]
failed

Solution

failed
failed

Solution Steps

Step 1: Understand the problem

The 8th graders want to raise at least $425 by selling chips and candy. They estimate selling at most 65 items per day. The earnings are $0.50 per bag of chips and $0.75 per bag of candy. Let \( x \) represent the total bags of chips sold and \( y \) represent the total bags of candy sold.

Step 2: Formulate the inequality for earnings

Since they want to raise at least $425, the total earnings from chips and candy must satisfy: \[ 0.50x + 0.75y \geq 425 \]

Step 3: Formulate the inequality for the number of items sold

They estimate selling at most 65 items per day, so the total number of items sold must satisfy: \[ x + y \leq 65 \]

Step 4: Compare with the given options

The correct system of inequalities is: \[ \begin{cases} 0.50x + 0.75y \geq 425 \\ x + y \leq 65 \end{cases} \] This matches option C.

Final Answer

The correct answer is C.

Was this solution helpful?
failed
Unhelpful
failed
Helpful