Advanced Algebra Practice Questions

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1. Find x+y, if: 5x+8y=67 and 2x-y=31 

a. 98
b. 46
c. 21
d. 14
e. 7

2. Peter’s salary is twice Ann’s salary and half of David’s salary. Then the average salary of Ann and David is             Peter’s salary.

a. equal to
b. larger than
c. depends on salary
d. there is no correct answer

3. Ann and Kate have 80 dollars together. If Kate buys ice-cream for 5 dollars, then  Kate will have double Ann’s money. How much money does Ann have?

a. $20
b. $25
c. $40
d. $50
e. $55

4. Given: a=b+2c,   b=3c. What is the average of numbers a,  b  and  c?

a. c
b. 1.5c
c. 2c
d. 2 1/3 c
e. 3c

5. In a forest  4/7 of all the trees are conifer and the rest are leaf-bearing. Among the leaf-bearing trees 7/15 are oak and 2/3 of these oaks are new. There are 160 old oaks in the forest. How many trees in all are in the forest?

a. 2400
b. 2800
c. 3200
d. 3600
e. 4000

6. Find x+y, if:    2x+3y=8 and 3x+5y=13 

a. 1.5
b. 2
c. 2.5
d. 3
e. 3.5

7. The speed of one car is  20%  less than the speed of a second car. What per cent more time does the first car need to travel the same route as the second car?

a. 12.5%
b. 20%
c. 25%
d. 30%
e. 33%

8. Number of boys in a class is twice the number of girls. 20% of the girls are brunettes and of the rest – half are blondes: Mary, Clara, Gina and Trisha. How many boys study in this class?

a. 20
b. 24
c. 30
d. 32
e. 40

9. In the previous question – what part of all the students are brunette girls?

a. 20%
b. 1/10
c. 1/2
d. 1/15
e. 15%

10. If the average of three numbers is V. If one of the numbers is Z and another is Y, what is the remaining number?

a. ZY – V
b. Z/V – 3 – Y
c. Z/3 – V – Y
d. 3V- Z – Y
e. V- Z – Y

11. Two cyclists start biking from a trail’s start 3 hours apart. The second cyclist travels at 10 miles per hour and starts 3 hours after the first cyclist who is traveling at 6 miles per hour. How much time will pass before the second cyclist catches up with the first from the time the second cyclist started biking?

a. 2 hours
b. 4 ½ hours
c. 5 ¾ hours
d. 6 hours
e. 7 ½ hours

12. Jim can fill a pool carrying buckets of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 1 ½ hours. How quickly can all three fill the pool together?

a. 12 minutes
b. 15 minutes
c. 21 minutes
d. 23 minutes
e. 28 minutes

13. Mary is reviewing her algebra quiz. She has determined that one of her solutions is incorrect. Which one is it?

a. 2x + 5 (x-1) = 9 x = 2
b. p – 3(p-5) = 10 p = 2.5
c. 4 y + 3 y = 28 y = 4
d. 5 w + 6 w – 3w = 64 w = 8
e. t – 2t – 3t = 32 t = 8

1. D

Find x+y, if: 5x+8y=67 and 2x-y=31

ChatGPT
To find the values of x and y, we can solve the given system of equations:

Equation 1: 5x + 8y = 67
Equation 2: 2x – y = 31

We can use the method of substitution or elimination to solve the system. Here, I’ll use the method of substitution:

From Equation 2, we can isolate y:
2x – y = 31
=> y = 2x – 31

Now substitute this value of y into Equation 1:
5x + 8(2x – 31) = 67
5x + 16x – 248 = 67
21x – 248 = 67
21x = 67 + 248
21x = 315
x = 315 / 21
x = 15

Substitute the value of x back into Equation 2 to solve for y:
2x – y = 31
2(15) – y = 31
30 – y = 31
-y = 31 – 30
-y = 1
y = -1

Therefore, the solution is x = 15 and y = -1.

To find x + y:
x + y = 15 + (-1) = 14

2. B

3. B

4. E

5. A

6. D

7. C

8. A

9. D

10. D

11. B

12. B

13. E