Primary School · Mathematics

Simple equations (Solving problems): Practice Questions

5 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Simple equations (Solving problems).

10 questions24 marksFree, no account

Question 1

1 mark

A taxi fare consists of a base fee of $24 plus $8 for every kilometer d traveled. If a passenger paid $88 in total, how many kilometers did they travel?

Question 2

1 mark

There are some apples in a basket. After adding 18 more apples, there are 50 apples in total. If \( n \) is the initial number of apples, which equation represents this situation and what is the value of \( n \)?

Question 3

1 mark

A bus started its journey with some passengers. At the first stop, 12 passengers got off and 5 passengers got on. At the second stop, half of the remaining passengers got off. There were 18 passengers left on the bus. Let \( p \) be the initial number of passengers. Solve the equation \( \frac{p - 12 + 5}{2} = 18 \) to find \( p \).

Question 4

1 mark

A bag of rice was shared equally into 6 containers. If each container has 4 kg of rice, let w be the total weight of rice in the bag. Solve the equation \( \frac{w}{6} = 4 \) to find the original weight.

Question 5

1 mark

Mr. Chan bought 5 identical notebooks and a pen that cost $12. He paid $67 in total. Find the price of one notebook by solving the equation \( 5x + 12 = 67 \), where \( x \) is the price of a notebook.

Question 6

2 marks

Solve the following equation for \( y \):
\( \frac{y}{4} + 11 = 20 \)

Write your answer out first, then check it against the worked solution.

Question 7

5 marks

Three-quarters of a number \( x \) is 15. Form an equation and find \( x \).

Write your answer out first, then check it against the worked solution.

Question 8

5 marks

A rectangular playground has a length of 25 m. If the perimeter is 80 m, find the width \( w \) of the playground by solving the equation \( 2(25 + w) = 80 \).

Write your answer out first, then check it against the worked solution.

Question 9

3 marks

A school organized a picnic for \(145\) students. They rented \(4\) large buses and \(3\) small vans. Each bus can carry \(x\) students, and each small van can carry \(15\) students. If all vehicles were full, find the capacity of one large bus.

(a) Write an equation to represent the situation using \(x\).
(b) Solve the equation to find the value of \(x\).

Write your answer out first, then check it against the worked solution.

Question 10

4 marks

A local bookstore is having a sale. A mystery novel costs $75. This is $15 more than \(\frac{3}{4}\) of the price of a hardback encyclopedia. Let \(x\) be the price of the encyclopedia.

a) Write an equation to represent the relationship between the mystery novel and the encyclopedia.
b) Solve the equation to find the price of the encyclopedia.

Write your answer out first, then check it against the worked solution.

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