Algebraic Equations Quiz

Henry has 5 packs of stickers, and each pack contains the same number of stickers. He also has 20 extra stickers. In total, he has 55 stickers. How many stickers are in each pack?

• 7 stickers

• 5 stickers

• 3 stickers

• 9 stickers

Answer explanation

To solve 5x + 20 = 55, subtract 20 from both sides to get 5x = 35. Then, divide by 5 to find x = 7. Thus, the correct answer is x = 7.

Michael has $15 in debt and he owes $11 for each hour he works. If he has $7 left after paying off his debt, how many hours did he work?

• x = -2

• x = 2

• x = -1

• x = 1

Answer explanation

To solve -11x - 15 = 7, first add 15 to both sides: -11x = 22. Then, divide by -11: x = -2. Thus, the correct answer is x = -2.

Liam is saving money to buy a new bicycle. He has already saved $8, but he needs $16 more to reach his goal. If he saves $6 each week, how many weeks will it take for Liam to reach his goal?

• 4 weeks

• -4 weeks

• 2 weeks

• -2 weeks

Answer explanation

To solve -6x + 8 = -16, subtract 8 from both sides to get -6x = -24. Then, divide by -6 to find x = 4. Thus, the correct answer is x = 4.

Maya has 18 apples and she buys 4 more apples every day. After a few days, she has a total of 6 apples. How many days did it take for Maya to have 6 apples?

• x = -3

• x = 3

• x = -2

• x = 2

Answer explanation

To solve 18 + 4x = 6, subtract 18 from both sides: 4x = 6 - 18, which simplifies to 4x = -12. Dividing by 4 gives x = -3. Thus, the correct answer is x = -3.

Jackson has $7 less than 9 times the amount of money he needs to buy a book. If he has $23, how much does he need to buy the book?

• x = 2

• x = -2

• x = 3

• x = -3

Answer explanation

To solve -7x - 9 = -23, add 9 to both sides: -7x = -14. Then, divide by -7: x = 2. Thus, the correct answer is x = 2.

Ethan is saving money to buy a new video game. He has already saved $12, but he needs $15 in total. If he saves $9 each week, how many weeks will it take for him to have enough money?

• 1/3 week

• 1/3 week

• 1/2 week

• 1/2 week

Answer explanation

To solve -9x + 12 = 15, subtract 12 from both sides: -9x = 3. Then, divide by -9: x = -1/3. Thus, the correct answer is x = -1/3.

David is buying packs of pencils. Each pack contains 2 pencils, and he needs a total of 60 pencils. How many packs does David need to buy?

• David needs 40 packs

• David needs 30 packs

• David needs 20 packs

• David needs 10 packs

Answer explanation

To solve 2(x - 10) = 60, first divide both sides by 2: x - 10 = 30. Then, add 10 to both sides: x = 40. Thus, the correct answer is x = 40.

Nora is organizing a charity event and needs to distribute gift bags. She has 6 times the number of gift bags as the number of volunteers plus 8 extra bags. If she ends up with 12 gift bags left after distribution, how many volunteers were there?

• 6 volunteers

• 4 volunteers

• 2 volunteers

• 0 volunteers

Answer explanation

To solve -6(x + 8) = -12, divide both sides by -6: x + 8 = 2. Then, subtract 8 from both sides: x = 2 - 8, which simplifies to x = -6. Thus, the correct answer is x = -6.

Sophia is organizing a party and needs to set up tables. She has 3 tables, and each table can seat x people. If she removes 7 seats from the total, she can seat 9 people. How many people can each table seat?

• x = 4

• x = 10

• x = 7

• x = 1

Answer explanation

To solve -3(x - 7) = 9, first divide both sides by -3, giving x - 7 = -3. Then, add 7 to both sides to find x = 4. Thus, the correct answer is x = 4.

Ethan is saving money to buy a new bicycle. He has already saved $8.60, but he needs $10 more to reach his goal. If he saves $2.40 each week, how many weeks will it take for Ethan to reach his goal?

• 7.5 weeks

• -7.5 weeks

• 5 weeks

• -5 weeks

Answer explanation

To solve -2.4x + 8.6 = -10, first subtract 8.6 from both sides: -2.4x = -18.6. Then, divide by -2.4: x = 7.5. Thus, the correct answer is x = 7.5.