Question

1. kadeem is going to an amusement park. the price of admission into the park is $30, and once he is inside the park, he will have to pay $2 for every ride he rides on. how much money would kadeem have to pay in total if he goes on 8 rides? how much would he have to pay if he goes on r rides?
2. parker went to the store to buy some cherries. the price per pound of the cherries is $3 per pound and he has a coupon for $2.25 off the final amount. with the coupon, how much would parker have to pay to buy 3 pounds of cherries? also, write an expression for the cost to buy p pounds of cherries, assuming at least one pound is purchased.
3. nabhitha is preheating her oven before using it to bake. the initial temperature of the oven is 65° and the temperature will increase at a rate of 25° per minute after being turned on. what is the temperature of the oven 15 minutes after being turned on? what is the temperature of the oven t minutes after being turned on?
4. leah has a cell phone plan that charges $40 per month and includes 200 international minutes, but then charges $2 per minute for every minute used over the included minutes. how much would leah have to pay in a month if she used 41 minutes over the limit? how much would leah have to pay in a month if she went over by x minutes?

Explanation:

Step1: Analyze the problem structure

For each problem, we have a fixed cost (or initial value) and a variable cost (or rate of change). We use the formula \(y = mx + b\) where \(m\) is the rate of change, \(x\) is the variable (number of rides, pounds, minutes etc.), and \(b\) is the fixed cost (or initial value).

Step2: Solve problem 32

• For 8 rides:

The fixed cost \(b = 30\) (admission), the rate \(m=2\) (cost per ride). Using the formula \(y=mx + b\), substitute \(x = 8\).
\(y=2\times8+30\)
\(y = 16+30\)
\(y=46\)

• For \(r\) rides:

Using the formula \(y=mx + b\), with \(m = 2\) and \(b = 30\), the expression is \(y=2r + 30\)

Step3: Solve problem 33

• For 3 pounds:

The rate \(m = 3\) (cost per pound), the fixed - adjustment \(b=- 2.25\) (coupon). Using the formula \(y=mx + b\), substitute \(x = 3\).
\(y=3\times3-2.25\)
\(y = 9 - 2.25\)
\(y=6.75\)

• For \(p\) pounds:

Using the formula \(y=mx + b\), with \(m = 3\) and \(b=-2.25\), the expression is \(y = 3p-2.25\)

Step4: Solve problem 34

• For 15 minutes:

The initial temperature \(b = 65\), the rate \(m = 25\) (temperature increase per minute). Using the formula \(y=mx + b\), substitute \(x = 15\).
\(y=25\times15+65\)
\(y=375+65\)
\(y = 440\)

• For \(t\) minutes:

Using the formula \(y=mx + b\), with \(m = 25\) and \(b = 65\), the expression is \(y=25t + 65\)

Step5: Solve problem 35

• For 41 minutes over the limit:

The fixed cost \(b = 40\), the rate \(m = 2\) (cost per over - limit minute). Using the formula \(y=mx + b\), substitute \(x = 41\).
\(y=2\times41+40\)
\(y=82 + 40\)
\(y=122\)

• For \(x\) minutes over the limit:

Using the formula \(y=mx + b\), with \(m = 2\) and \(b = 40\), the expression is \(y=2x + 40\)

Answer:

• Problem 32:
• If he goes on 8 rides, he pays \(\$46\).
• If he goes on \(r\) rides, he pays \((2r + 30)\) dollars.
• Problem 33:
• If he buys 3 pounds, he pays \(\$6.75\).
• If he buys \(p\) pounds, he pays \((3p-2.25)\) dollars.
• Problem 34:
• 15 minutes after being turned on, the temperature is \(440^{\circ}\).
• \(t\) minutes after being turned on, the temperature is \((25t + 65)^{\circ}\).
• Problem 35:
• If she used 41 minutes over the limit, she pays \(\$122\).
• If she goes over by \(x\) minutes, she pays \((2x + 40)\) dollars.