College Math Prep. A (2021) Unit Exam One

Jodi is choosing between two restaurants. Big Buffet charges $16.95 for an entrée plus $2.95 per trip to the salad bar. King Buffet charges $13.95 for an entrée plus $4.95 per trip to the salad bar. If she makes her decision solely on price, which restaurant should she choose if she plans to make 2 trips to the salad bar?

Big Buffet, because it will cost $22.85

Laura, Dale, Haley, and Rick are choosing their seats in a row at the movies. You need to find the order in which they must sit according to these conditions: Neither Haley nor Laura like Rick. The girls want to sit next to each other. Dale will sit between a boy and a girl. Haley will sit in the far-right seat. After analyzing the problem, what is a good process for solving it?

Draw a picture, because this problem involves a physical layout.

On the night shift in a hospital ward, the ratio of doctors to nurses is 2:3, and 15 people are working. How can this problem be modeled to find the number of nurses on duty?

Make two tape diagrams, one with 2 rectangles and one with 3 rectangles. Label the diagrams with "15 people."

Jackson is 14 years old, and his sister Marie is twice his age. He wants to know how old Marie will be when he is 28. How can Jackson use the given information to determine his sister's age when he is 28?

Marie is twice his age, so he can double his age to find her current age. He can then determine the number of years it takes for him to reach 28 and add that number to Marie's current age.

Mrs. Cooper asks two painters for a price quote to paint her house. Steve charges $400 plus $30 per gallon of paint used. Max charges $300 plus $40 per gallon of paint. If 5 gallons are required for the job, who offers the better price? How do you know? Select the option that correctly answers both questions

Max, because Steve will charge $550 and Max will charge $500

Mia owns a new cupcake shop. On opening day, she served 30 customers. On the next three days she served 50, 80, and 120 customers, respectively. What is an appropriate strategy for Mia to use to predict how many customers she will serve on the seventh day?

Mia should subtract the number of customers from the previous day from the number on each day to find a pattern. Then she should continue that pattern three more times to find the number of customers on the seventh day.

The sum of two consecutive numbers is 27. What strategy could you use to find the two numbers?

Pick a set of two numbers that follow each other and check that they add to 27. Continue using trial and error until you find the correct pair of numbers.

Mrs. Teller earns $400 a week as a day nanny for the Smith family. When she must also stay with the children overnight, she earns an additional $25 per night. How much would she earn for a week with 3 overnights? Examine the following steps used to solve the problem. The solution contains an error. What is an appropriate problem-solving strategy that gives the correct solution?

Use the equation P = 400 + 25n, where P is total pay and n is the number of overnights. Then substitute n = 3 to get the value of P.

A concrete block with a mass of 14.5 kg is pushed with a force of 80 Newtons. What is a valid process for finding the acceleration of the block?

Use the formula F = ma. Substitute 80 for F and 14.51 for m, then solve for a using inverse operations.

Olivia wants to spend more time reading for pleasure over summer break. In the first week, she reads for 15 minutes per day. She plans to increase her daily reading time by 3 minutes at the start of each new week. If she reads five days per week, what is an appropriate process for finding the total number of minutes she will read in week 5?

XXX Create a bar graph with the number of weeks on the x-axis and the number of minutes read on the y-axis. Make the first bar 15 minutes, then add 3 minutes to get the height of the next bar. Continue that pattern through week 5.

Antoine is renting a car for a day to drive to his sister's college and back. He estimates that the college is about 60 miles away. Low Price Rentals charges a $49 rental fee plus $0.16 per mile driven. Easy Rental charges a $25 fee plus $0.50 per mile. Compare the two rental options. Which company offers a better deal? How do you know? Select the option that correctly answers both questions.

XXX Easy Rental, because it will charge $55.00 for the trip, while Low Price Rentals will charge $58.60

A robot travels in a straight line 12 feet, makes a 90-degree turn, then travels in another straight line 5 feet. Pat needs to find the distance between the robot's starting and ending points. Examine Pat's drawing, which shows a right triangle and labels for the sides.

XXX Substitute a = 5 and c = 12 into a2 + b2 = c2 to find the length of the third side.

A magician puts on a show at a local restaurant that charges him $350 to use the stage. He sells show tickets that cost $14 per adult, $6 per child, and $2 per senior citizen. If he sells 16 adult tickets and 6 senior citizen tickets, how many children's tickets will he need to sell to cover the stage rental cost? After analyzing the problem, what is an appropriate process for solving it?

XXX The magician sells 16 adult tickets for $14 each and 6 senior tickets for $2 each, and he needs $350. Find 350 − 14(16) + 2(6). Divide the result by 6 to find the number of children's tickets he must sell. Check the answer by finding the combined sum of money he makes on each type of ticket, which should equal $350.

On her lunch break, Eden visits two food courts where she can build her own salad. At both locations, the cashier weighs the salad to calculate the cost. Lunch Rush charges $1.50 for the container and $0.59 per ounce. Healthy Bites does not charge for the container but charges $0.99 per ounce. Calculate the cost of a salad at each location for 1 ounce, 2 ounces, 3 ounces, 4 ounces, and 5 ounces. When does the cost at Healthy Bites become more expensive than Lunch Rush?

XXX at 5 ounces

Lexi needs to hire a plumber to replace a toilet. XYZ Plumbing charges $29 for the service call plus $75 per hour for labor. Pipe Dreams Plumbing charges $125 for the service call plus $25 per hour for labor. Find the cost of each service, assuming the job will take 3 hours. Which plumber is more expensive? How do you know? Select the option that correctly answers both questions.

XYZ, because it will cost $254, while Pipe Dreams will cost $200

A party planner is decorating for a hockey-themed birthday party. She places hockey pucks in layers, adding a puck to each layer, to create a triangular tower of hockey pucks. What is an appropriate model for her to use to find how many pucks will be in a display that has 6 layers?

a sketch of hockey pucks, adding 1 puck per layer so the pucks are stacked in a triangular shape until there are 6 layers

Casey is sorting his coin collection into two different cases, one for US coins and the other for foreign coins. The ratio of US coins to foreign coins is 4:3, and he has 63 coins in his collection. What is an appropriate model for Casey to use to find out how many of his coins are foreign?

a tape diagram with 4 rectangles to represent US coins for every 3 rectangles to represent foreign coins until there are 63 rectangles

Isaiah subscribes to a music streaming service that charges $5.99 a month plus $0.79 for each song that he downloads to his device. Which equation represents his cost in a month, c, if he downloads s songs?

c = 0.79s + 5.99

Bobbie bought a jacket for 25% off. If the price they paid was $57, what equation can be used to find the original price of the jacket?

c − 0.25c = 57, where c is the original price of the jacket

It took George 3 hours to drive 150 miles. Using context clues from the problem, what formula can be used to find George's rate of speed?

d = rt