# Advanced Algebra Practice Questions

- Posted by Brian Stocker MA
- Date October 18, 2012
- Comments 9 comments

### Advanced Algebra

### Advanced Algebra Problems

**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

### Advanced Algebra Problems – Answer Key

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

**Written by**, Brian Stocker MA., Complete Test Preparation Inc.

**Date Published:**Thursday, October 18th, 2012

**Date Modified:**Monday, July 1st, 2024

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## 9 Comments

nice! thanks

Can you show how to solve them with the answers cuz sum of them are hard

thanks! corrected

Can you please show the solution how they get the answer?

question 1)

5x+8y=67…..(1)

2x-y=31……….(2)

multiply equation 2 by 8

16x-8y=248…..(3)

solve equations (1) and (3)

5x+8y=67

16x-8y=248

after solving these 2 equations

21x=315 so x=15

put value of x in any equation 1 or 2

2x-y=31 so we will get

30-y=31 so y=-1

final answer x+y is 15-1=14

Answer =14

thank you so much

ChatGPT — See if you can spot the Error!

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.

Let’s assign variables to the salaries of Ann, Peter, and David.

Let A represent Ann’s salary.

Then, Peter’s salary is 2A (twice Ann’s salary).

David’s salary is 2 * (2A) = 4A (twice Peter’s salary).

To find the average salary of Ann and David, we add their salaries and divide by 2:

(A + 4A) / 2 = 5A / 2

We are given that this average salary is equal to Peter’s salary (2A):

5A / 2 = 2AINCORRECT! After this the whole thing is wrong!To solve for A, we can multiply both sides of the equation by 2:

5A = 4A

Subtracting 4A from both sides:

5A – 4A = 4A – 4A

A = 0

Since the average salary and Peter’s salary are both multiples of A, if A is zero, it implies that all the salaries are zero. However, this does not make sense in the context of the problem.

Therefore, there seems to be an inconsistency in the information provided. Please double-check the problem statement for accuracy.

As soon as you see 5A=4A you know something has gone wrong.

5A/2 = 2.5A

2.5A>2A

ChatGPT – MORE CHATGPT ERRORSLet’s assume Ann has x dollars. Since Ann and Kate have a total of 80 dollars, we can write the equation:

x + Kate’s money = 80

After Kate buys ice-cream for 5 dollars, she will have double Ann’s money:

Kate’s money – 5 = 2 * Ann’s money

We can substitute the value of Kate’s money from the first equation into the second equation:

(x + Kate’s money) – 5 = 2x INCORRECT!!SHOULD be (Kate’s money – 5) = 2xAfter this it goes off the rails

CORRECT EQUATIONSKate’s money – 5 = 2 * Ann’s money

Ann’s Money = x

The 2 Equations are:

Kate’s money – 5 = 2 * Ann’s Money

Kate’s money = 80 – x

(80 – x) – 5 = 2x

80 – x = 2x – 5

80 = 3x -5

(80- 5) = 3x

x = 25