EOC Practice #1

John designs computer labs for a community college. The

college has 115 computers and receives 26 additional

computers each year. What expression can Sue use to

determine the number of computers the college will

have in n years?

Answer explanation

Start with 115 computers.

Receive 26 additional each year.

n = number of years

26n + 115

Kaye want to make trail mix made up of almonds, walnuts, and raisins. She wants to mix one part almonds, three parts walnuts, and four parts raisins. Almonds cost $10 per pound, walnuts cost $12 per pound, and raisins cost $6 per pound.

Kaye has $25 to spend on the trail mix. Determine how many pounds of trail mix she can make.

Answer explanation

Let x = pounds of an ingredient

1 almonds: 3 walnuts: 4 raisins

1:3:4

1x + 3x + 4x = 8x pounds of mix

10(x) + 12(3x) + 6(4x) = 25

70x = 25

x = 25/70 = 5/14

8(5/14) = 2 6/7

Kaye can make 2 6/7 lbs of trail mix.

A rectangular garden measuring 15 meter by 12 meters is to have a walkway installed around it with a width of x meters, as shown in the diagram below. Together, the walkway and the garden have an area of 378 square meters. Write an equation (using factors) that can be used to find x, the width of the walkway.

Answer explanation

x = width of walkway

One side of the garden including walkway = 2x+12

Other side of the garden including walkway = 2x +15

Area is 378

Length x Width = Area

(2x + 12)(2x +15) = 378

An animal shelter spends $3.45 per day to care for each cat and $6.50 per day to care for each dog. Pat noticed that the shelter spent $92.20 caring for cats and dogs on Wednesday. Pat said that there might have been 8 cats and 14 dogs at the shelter on Wednesday. Are Pat’s numbers possible? Create an equation to represent the possible number of cats and dogs that could have been at the shelter on Wednesday and use it to justify you answer.

Answer explanation

c = cats d = dogs

$3.45 to care for cats $6.50 to care for dogs

Total spent = $92.20

3.45c + 6.50d = 92.20

3.45(8) + 6.50(14) = 92.20

118.60 ≠ 92.20

It is not possible for there to have been 8 cats and 14 dogs at the shelter Wednesday.

The Freshman Spirit Club took a trip to the state fair. There were 59 Students and 6 chaperones, and the total admission cost for the groups was $508. Student tickets cost $2 more than chaperone tickets.

Write and solve an equation to find the cost of a student ticket. Show your work and explain the meaning of your variable.

Answer explanation

Students = 59 Chaperones = 6

Total Admission = $508

Student Tickets = $2 + Chaperone Tickets

Let c = Chaperone Tickets

508 = 6c + 59(2 + c)

Chaperone tickets = $6

Therefore student tickets cost $8

A number n is divided by 9 is 3. What is the remainder when 3n + 5 is divided by 9?

Answer explanation

n/9=3, so therefore n=27

Substitute n for 27:

3(27)+5

Solve and then divide by 9 and the remainder is:

3(27) + 5 = 86

86÷9= 9 r 5

So the remainder is 5.

A company uses two different-sized trucks to deliver sand. The first truck can transport x cubic yards, and the second y cubic yards. The first truck makes S trips to a job site, while the second makes T trips. What quantities do the following expressions represent in terms of the problem’s context?

xS + yT

Answer explanation

1st truck transports x cubic yards and makes S trips.

2nd truck transports y cubic yards and makes T trips.

xS is the total amount delivered by the 1st truck

yT is the total amount delivered by the 2nd truck

So xS + yT is the total amount delivered by both trucks

Ms. Jones is taking the Drama Club on a field trip to see the musical Phantom of the Opera. The school treasurer asked Ms. Jones for the group’s total ticket cost. He wrote the following cost function for the school treasurer:

Total Cost = 53 (40 + 4)

Which of the following statements best describes this cost function?

• A total of 53 people, which included 40 students and 4 teachers, will attend the field trip.

• The bus fits 53 people, including 40 students and 4 teachers.

• Tickets cost $53 each, and there are 40 students and 4 teachers going on the field trip.

• The school will buy 53 tickets for the musical. Tickets cost $40 for each student and $4 for each teacher.

Answer explanation

40 represents the amount of students

4 represent the amount of teachers

The total people attending is 44.

The 53 represents the amount of cost for the tickets.

So 53(44) = $2,332 which represents the total amount for the tickets.

A shoe store is having a sale in which all tennis shoes are $25. The sales tax is 7%. If Dan buys n tennis shoes during this sale, the total cost of his purchase will be 25n + 0.07(25n). Interpret the meaning of 0.07(25n) in this context.

Last weekend, Cindy purchased two tops, a pair of pants, and a skirt in her favorite store. The equation T = 1.075x can be used to calculate her total cost where x represents the pretax subtotal cost of her purchase.

In the equation T = 1.075x, what does the number “1” represent? Explain using the context of Cindy’s situation.

In the equation T = 1.075x, what does the number “0.075” represent? Explain using the context of Cindy’s situation.