5. If a person's salary increases from $200 per week to $234 per week, what is the

percent increase in the person's salary?

6.If an athlete's weight decreases from 160 pounds to 152 pounds, what is the percent

decrease in the athlete's weight?

7.A particular stock is valued at $40 per share. If the value increases by 20 percent and

then decreases by 25 percent, what will be the value of the stock per share after the

decrease?

8.There are a total of 20 dogs and cats at a kennel. If the ratio of the number of dogs to

the number of cats at the kennel is 3 to 2, how many cats are at the kennel?

9.The integer cis even, and the integer dis odd. For each of the following integers,

(a) c + 2 cd

(b) 2c +d

(c) cd (d) cd

(e) (c + d)2

(f) c2 - d2

10.When the positive integer nis divided by 3, the remainder is 2, and when nis divided

by 5, the remainder is 1. What is the least possible value of n?

1.Find an algebraic expression to represent each of the following. (a) The square of y is subtracted from 5, and the result is multiplied by 37.

(b) Three times x is squared, and the result is divided by 7.

(c) The product of 4x+ and y is added to 18.

2. Simplify each of the following algebraic expressions

a) 3x2 - 6 + x + 11 -x2 +5x

b) 3(5x-1) -x +4

c) x2-4/x-4, where x = 4

d) (2x + 5) (3x-1)

3. Use the rules of exponents to simplify the following.

a) (n^5) (n^-3)

b) (s^7) (t^7)

c) r^12/r^4

d) (2/b) ^5

e) (w^5) ^-3 f) (5^0) (d^3) g) (x1^0) (y^-1)/(x^-5) (y^5)

h) (3/2) ^2 (1/y) ^5

4. Solve each of the following systems of equations for x and y.

a) x + y = 24, x - y = 18

b) 3x - y = -5, x + 2y = 3

c) 15x -18 - 26 = -3x +y, 10x +7y +20 = 4x + 2

5. Solve each of the following inequalities for x.

a) -3x > 7 + x

b) 25x + 16 10 - x

c) 16 + x > 8x -12

6. For a given two-digit positive integer, the tens digit is 5 more than the unit's digit. The sum of the digits is 11. Find the integer.

7.If the ratio of 2x to 5y is 3 to 4, what is the ratio of x to y?

8.Kathleen's weekly salary was increased by 8 percent to $712.80. What was her weekly

salary before the increase?

9.A theater sells children's tickets for half the adult ticket price. If 5 adult tickets and 8 children's tickets cost a total of $81, what is the cost of an adult ticket?

10.Pat invested a total of $3,000. Part of the money was invested in a money market account that paid 10 percent simple annual interest, and the remainder of the money was invested in a fund that paid 8 percent simple annual interest. If the total interest earned at the end of the first year from these investments was $256, how much did Pat invest at 10 percent and how much at 8 percent?

11.Two cars started from the same point and traveled on a straight course in opposite directions for 2 hours, at which time they were 208 miles apart. If one car traveled, on average, 8 miles per hour faster than the other car, what was the average speed of each car for the 2-hour trip?

12.A group can charter a particular aircraft at a fixed total cost. If 36 people charter the aircraft rather than 40 people, then the cost per person is greater by $12.

(a) What is the fixed total cost to charter the aircraft?

(b) What is the cost per person if 40 people charter the aircraft?

13.An antiques dealer bought c antique chairs for a total of x dollars. The dealer sold each chair for y dollars. (a) Write an algebraic expression for the profit, P, earned from buying and selling the chairs. (b) Write an algebraic expression for the profit per chair.

Ratios & Proportions Simplify each ratio 1) 40:15

2)49:7

Find the UNIT RATE for each

3) 80 inches over 10 days

4) 3 ounces cost $2.73 5) 10-ounce jar of peanut butter is $3.90

6) 12 boxes can hold 96 books

Decide if each pair of ratios forms a proportion

7) 12/6 and 4/2

8) 34 and 9/20

9) 4/2 and 8/6

10) 12/8 and 3/2

Solve each proportion

11) 4/5 =n/2

12) x/9 =2/6

13) 5/b =9/5

14) b/3 =4/10

Answer each question and round the answer to the nearest whole number

15) If you can buy one bunch of seedless green grapes for $2, then how many can you buy with $16?

16) One package of blueberries costs $3. How many packages can you buy for $9?

17) The currency in the eastern Caribbean islands is the Eastern Caribbean Dollar. The exchange rate is approximately $1 to 3 Eastern Caribbean Dollars. At this rate, how many Eastern Caribbean Dollars would you get if you exchanged $5?

18) Abhasra took a trip to Malaysia. Upon leaving she decided to convert all of her Ringgits back into dollars. How many dollars did she receive if she exchanged 24 Ringgits at a rate of 4 Ringgits to $1?

19) A frame is 4 in tall and 2 in wide. If it is enlarged to a width of 6 in , then how tall will it be?

20) Elisa reduced the size of a frame to a height of 2 in. What is the new width if it was originally 4 in tall and 8 in wide?

Linear Systems: Multiple Choice

1) Which linear system has the solution x = -2 and y = 6?

a. x+3y=16, 4x+4y=16 b. x+3y=17, 2x + y = 15 c. x+2y=-2, 2x+4y =-4

d. 2x+y=-2, x + y = 16

2) Create a linear system to model this situation:

A collection of nickels and dimes contains four times as many dimes as nickels. The total

value of the collection is $20.25.

a. d=4n, 5n + 10d = 2025

b. d=4n, 5d + 10n = 2025

c. n=4d, 5n+10d = 2025

d. d+n=15, 5n+10d= 2025

3) Create a linear system to model this situation:

A woman is 3 times as old as her son. In thirteen years, she will be 2 times as old as her

son will be.

a. w=s+3, w + 13 = 2s b. w=3s, w + 13 = 2(s + 13) c. w=3s, w = 2s d. w=3s, s + 13 = 2(w + 13)

4) Create a linear system to model this situation: Tickets for a school play cost $8 for adults and $4.75 for students.

a. 8a+4.75s=1399, s = a + 10

b. 8a+4.75s=1399, a + s = 10

c. 8a+4.75s=1399, a = s + 10

d. 4.75a+8s=1399, s = a + 10

5)Write an equivalent system with integer coefficients. 5x + 3/2 y = 1 4, 5x + 5y = 755/66

a. 10x+3y=1, 5x+30y=1 b. 3x+10y=28, 5x+30y=755 c. 10x+3y=28, 30x+5y=755 d. 10x+3y=28, 5x+30y=755 6) Determine the number of solutions of the linear system: 14x - 5y = 123, 14x - 5y = 73

a. no solution

b. infinite solutions

c. two solutions d. one solution

8) Determine the number of solutions of the linear system: 14x + 7y = 315, 16x - 2y = 610

a. no solution b. one solution c. two solutions d. infinite solutions

Short Answers

11. Create a linear system to model this situation:

Solve this linear system by graphing. -3x -2y = 16, -x + y = -8

Two ships start sailing towards each other at the same time from two islands that are 365

km apart. One ship travel 5 km/h faster than the other. They meet in 5 h. What is the

average speed of each ship? Verify that 34 km/h and 39 km/h represent the solution of the

linear system.

14) For what values of k does the linear system below have:

a) infinite solutions? b) one solution? c) no solution?

kx + 3y = 48.

2/3 x + y = 16

16) Use substitution method to solve this linear system. x=4+y, 4x + 16y = -264

17) Use substitution method to solve this problem:

The perimeter of a rectangular field is 276 m. The length is 18 m longer than the width.

What are the dimensions of the field?

18) Use an elimination strategy to solve this linear system. 4x 3y = 10, 2x + 5y = 18.

19) Use an elimination strategy to solve this linear system. 3x 2y = 5, 2x + 7y = 20.

21) Use an elimination strategy to solve this linear system. 20x 24y = 52, 8x + 32y =

104

20) Use an elimination strategy to solve this linear system. 2/3 m + 3/4 n = 16

1 /2m + 3/8 n =18