A group of students wants to sell T-shirts as a fundraiser. To manufacture the T-shirts, it will cost the students a one-time fee of $150, plus $5 for each T-shirt sold. They plan to sell the T-shirts for $12 each.

Which of the following equations correctly describes Y, the number of dollars raised by students in terms of x, the number of t-shirts sold?

Let's analyze the table to determine the relationship between slices of cake and calories.

We’ll use two points to find the calories per slice:

From the table:

• At 2 slices → 960 calories
• At 5 slices → 2,400 calories

Step 1: Find the difference

2,400−960=1,440caloriesincreasefor5−2=3slices

1,4403=480caloriesperslice

We can verify this with another pair:

• At 11 slices: 11×480=5,280
• At 19 slices: 19×480=9,120

Everything checks out.

Correct answer: C. Each slice of cake is 480 calories.

Let's rule out the others:

• A. Says 960 calories per slice — wrong.
• B. Says it's a negative relationship — incorrect, it’s positive.
• D. Claims no direct relationship — incorrect, it’s a linear relationship.

We are asked to find an equation for Y, the profit (or dollars raised), based on:

• Selling price per T-shirt: $12
• Cost per T-shirt: $5
• One-time fixed cost: $150
• Number of shirts sold: x

Step-by-step breakdown:

• Total Revenue:

Revenue=12x

• Total Cost:

Cost=150+5x

• Profit (Y) = Revenue – Cost:

Y=12x−(150+5x)

Correct answer: D. Y = 12x – (5x + 150)

Explanation

We are given:

• Pool C drains in 6 hours
• Pool B takes 3 times as long as Pool C →

B=3×6=18hours

• Pool B takes twice as long as Pool A →

A=182=9hours

Correct answer: D. 9

We are told:

• Initial population = 1,000
• The bacteria doubles every 3 days
• We want the population after 9 days

Step 1: Determine how many doubling periods in 9 days

9/3=3doublings

Step 2: Double the population 3 times

Populationafter9days=1000×23=1000×8=8000

Correct answer: B. 8,000

We are given:

• Monthly income: $2,586.00
• Deductions:
  • Insurance: $517.20
  • Federal taxes: $299.33
  • Social security: $156.69
  • State taxes: $99.77

Step 1: Add all deductions

517.20+299.33+156.69+99.77=1,072.99

Step 2: Subtract from gross income

2,586.00−1,072.99=1,513.01

Correct answer: C. $1,513.01

Let's convert all values to decimals to compare them:

1. 3/4 = 0.75
2. 70% = 0.70
3. 5/7 ≈ 0.714
4. 0.79 = 0.79

Now, arrange from least to greatest:

• 70% (0.70)
• 5/7 (≈0.714)
• 3/4 (0.75)
• 0.79

Final Answer (in order from least to greatest):

70%, 5/7, 3/4, 0.79

Let’s define the total cost for each restaurant:

• Restaurant A: Charges $100 + $20 per person

CostA=100+20x

• Restaurant B: Charges $25 + $25 per person

CostB=25+25x

We want to find the number of people x where the costs are equal:

Step 1: Set the costs equal

100+20x=25+25x

Step 2: Solve for x

Subtract 20x from both sides:

100=25+5x

Subtract 25 from both sides:

75=5x

Divide by 5:

x=15

We are given:

• Each person drinks 3 boxes of juice
• 38 people at the picnic
• 6 boxes per package

Step 1: Total boxes needed

38people×3boxesperperson=114boxes

Step 2: Number of packages needed

114boxes/6boxesperpackage=19packages

Best estimate (rounding up to ensure enough juice):

20packages

Correct answer: A. 20 packages

We are given:

• 1 gallon = 16 cups

• 1 cup = 16 tablespoons

So:

Step 1:

1/2gallon=8cups

Corrected Step 2:

8cups×16tbsppercup=128tablespoons

Correct answer: A. 128 tablespoons

To find which fraction is between 2/3 ​ and 4/5, we can convert all fractions to decimals:

• 23≈0.666…
• 45=0.8

Now evaluate each option:

• A. 78=0.875 → Too big
• B. 57≈0.714 → Between
• C. 35=0.6 → Too small
• D. 58=0.625 → Too small

Correct answer: B. 5/7