Question

1. a caterer charges $120 to cater a party for 15 people and $200 for 25 people. assume that the cost, y, is a linear function of the number of x people. write an equation in slope - intercept form for this function. what does the slope represent? how much would a party for 40 people cost?
2. attorney a charges a fixed fee on $250 for an initial meeting and $150 per hour for all hours worked after that. write an equation in slope - intercept form. attorney b charges $150 for the initial meeting and $175 per hour. find the charge for 26 hours of work for each attorney. which is the better deal? at how many hours does this attorney become a better deal?
3. a water tank already contains 55 gallons of water when baxter begins to fill it. water flows into the tank at a rate of 8 gallons per minute. write a linear equation to model this situation. find the volume of water in the tank 25 minutes after baxter begins filling the tank
4. a video rental store charges a $20 membership fee and $2.50 for each video rented. write and graph a linear equation (y = mx + b) to model this situation. if 15 videos are rented, what is the revenue? if a new member paid the store $67.50 in the last 3 months, how many videos were rented?
5. casey has a small business making dessert baskets. she estimates that her fixed weekly costs for rent and electricity are $200. the ingredients for one dessert basket cost $2.50. if casey made 40 baskets this past week, what were her total weekly costs? her total costs for the week before were $562.50. how many dessert baskets did she make the week before?

Explanation:

Step1: Find the linear equation for the video rental store problem

The slope - intercept form is \(y = mx + b\). Here, the membership fee \(b=\$20\) (the initial cost when \(x = 0\)), and the cost per video \(m=\$2.50\). So the equation is \(y=2.5x + 20\).

Step2: Calculate the revenue for 15 videos rented

Substitute \(x = 15\) into the equation \(y=2.5x + 20\).

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Step3: Find the number of videos rented when \(y = 67.50\)

Substitute \(y = 67.50\) into \(y=2.5x + 20\) and solve for \(x\).

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Answer:

The linear equation is \(y = 2.5x+20\). The revenue for 15 videos rented is \(\$57.50\). The number of videos rented when the payment is \(\$67.50\) is \(19\).