# Algebra Practice Test 1

1. 5/p
2. p – 5
3. p + 5
4. p/5
5. 1- p + 5
##### 2. If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?
1. 2 hours and 24 minutes
2. 3 hours and 12 minutes
3. 3 hours and 44 minutes
4. 4 hours and 10 minutes
5. 4 hours and 33 minutes
1. \$280.90
2. \$287.00
3. \$292.50
4. \$306.00
5. \$333.89
1. \$14,310.40
2. \$14,990.90
3. \$15,290.70
4. \$15,737.50
5. \$16,935.80
1. -2.4
2. 2.4
3. 1.3
4. -1.3
5. 0
1. 8
2. 10
3. 14
4. 19
5. 21
1. \$240
2. \$480
3. \$720
4. \$960
5. \$1,200
1. \$496.30
2. \$512.40
3. \$555.40
4. \$574.90
5. \$588.20
1. 10
2. 11 cents
3. 15 cents
4. 17 cents
5. 21 cents
1. 2.7
2. 2.8
3. 3.0
4. 3.1
5. 3.2
1. \$120.25
2. \$160.75
3. \$173.75
4. \$180.00
5. \$182.50
1. 4
2. 8
3. 12
4. 13
5. 16
1. y
2. 2y
3. 4y
4. 10y
5. 15y
1. 150/x
2. 150x
3. 6x
4. 1500/x
5. 600x
1. \$57
2. \$90
3. \$104
4. \$112
5. \$122
1. 12
2. 25
3. 33
4. 47
5. 86
1. \$5.20
2. \$7.35
3. \$13.40
4. \$19.95
5. \$21.25
1. \$3225
2. \$4350
3. \$5375
4. \$6550
5. \$6398
1. \$132.85
2. \$145.75
3. \$162.90
4. \$225.25
5. \$226.75
##### 20. If y = 3, then y3(y3-y)=
1. 300
2. 459
3. 648
4. 999
5. 1099

###### 1. A

The following proportion may be written: 1/p=x/5. Solving for the variable, x, gives xp = 5, where x=5/p. So, Lynn can type 5/p pages, in 5 minutes.

###### 2. A

Sally can paint 1/4 of the house in 1 hour. John can paint 1/6 of the same house in 1 hour. In order to determine how long it will take them to paint the house, when working together, the following equation may be written: 1/4 x+1/6 x=1. Solving for x gives 5/12 x=1, where x= 2.4 hours, or 2 hours, 24 minutes.

###### 3. D

Sale Price = \$450 – 0.15(\$450) = \$382.50, Employee Price = \$382.50 – 0.2(\$382.50) = \$306

###### 4. D

\$12,590 = Original Price – 0.2(Original Price) = 0.8(Original Price), Original Price = \$12,590/0.8 = \$15,737.50

###### 5. A

In order to solve for A, both sides of the equation may first be multiplied by 3. This is written as 3(2A/3)=3(8+4A) or 2A=24+12A. Subtraction of 12A from both sides of the equation gives -10A=24. Division by -10 gives A = -2.4.

###### 6. A

Three equations may initially be written to represent the given information. Since the sum of the three ages is 41, we may write, l + s + j = 41, where l represents Leah’s age, s represents Sue’s age, and j represents John’s age. We also know that Leah is 6 years older than Sue, so we may write the equation, l = s + 6. Since John is 5 years older than Leah, we may also write the equation, j = l + 5. The expression for l, or s + 6, may be substituted into the equation, j = l + 5, giving j = s + 6 + 5, or j = s + 11. Now, the expressions for l and j may be substituted into the equation, representing the sum of their ages. Doing so gives: s + 6 + s + s + 11 = 41, or 3s = 24, where s = 8. Thus, Sue is 8 years old.

###### 7. E

Simple interest is represented by the formula, I = Prt, where P represents the principal amount, r represents the interest rate, and t represents the time. Substituting \$4,000 for P, 0.06 for r, and 5 for t gives I = (4000)(0.06)(5), or I = 1,200. So, he will receive \$1,200 in interest.

###### 8. A

\$670 = Cost + 0.35(Cost) = 1.35(Cost), Cost = \$670/1.35 = \$496.30

###### 9. D

The amount of taxes is equal to \$55*0.003, or \$0.165. Rounding to the nearest cent gives 17 cents.

###### 10. C

The GPA may be calculated by writing the expression, ((3*2)+(4*3)+(2*4)+(3*3)+(4*1))/13, which equals 3, or 3.0.

###### 11. C

From 8:15 A.M. to 4:15 P.M., he gets paid \$10 per hour, with the total amount paid represented by the equation, \$10*8=\$80. From 4:15 P.M. to 10:30 P.M., he gets paid \$15 per hour, with the total amount paid represented by the equation, \$15*6.25=\$93.75. The sum of \$80 and \$93.75 is \$173.75, so he was paid \$173.75 for 14.25 hours of work.

###### 12. D

If she removes 13 jellybeans from her pocket, she will have 3 jellybeans left, with each color represented. If she removes only 12 jellybeans, green or blue may not be represented.

###### 13. A

The value of z may be determined by dividing both sides of the equation, r=5z, by 5. Doing so gives r/5=z. Substituting r/5 for the variable, z, in the equation, 15z=3y, gives 15(r/5)=3y. Solving for y gives r = y.

###### 14. A

50 cents is half of one dollar, thus the ratio is written as half of 300, or 150, to x. The equation representing this situation is 300/x*1/2=150/x.

###### 15. B

The following proportion may be used to determine how much Lee will make next week: 22/132=15/x. Solving for x gives x = 90. Thus, she will make \$90 next week, if she works 15 hours.

###### 16. C

The given equation should be solved for x. Doing so gives x = 6. Substituting the x-value of 6 into the expression, 5x + 3, gives 5(6) + 3, or 33.

###### 17. C

The amount you will pay for the book may be represented by the expression, 80+(80*0.0825). Thus, you will pay \$86.60 for the book. The change you will receive is equal to the difference of \$100 and \$86.60, or \$13.40.

###### 18. B

The amount you have paid for the car may be written as \$3,000 + 6(\$225), which equals \$4,350.

###### 19. A

You will need 40 packs of pens and 3 sets of staplers. Thus, the total cost may be represented by the expression, 40(2.35) + 3(12.95). The total cost is \$132.85.

###### 20. C

Substituting 3 for y gives 33 (33-3), which equals 27(27 – 3), or 27(24). Thus, the expression equals 648.