Multiple Variables: Problem Solving & Reasoning
Mathematics
Grade 7
15 questions
~30 mins
1 views0 downloads
About This Worksheet
A worksheet focused on solving problems involving multiple variables with substitution, designed to develop reasoning and application skills for Grade 7 students.
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Full preview • 15 questions
Multiple Variables: Problem Solving & Reasoning
Subject: MathematicsGrade: Grade 7
Name:
Date:
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Untitled Worksheet
Grade Grade 7
A
Fluency & Practice
Solve the following questions by substituting the given values. Show your working in the grid spaces provided.
1.
Given x=3 and y=4, find the value of 2x + 3y.
[2 marks]2.
If m=5 and n=2, calculate m^2 + 4n.
[2 marks]3.
Using x=2, y=7, evaluate 3x + 2y.
[2 marks]4.
Calculate the value of 4a + 3b when a=6 and b=1.
[2 marks]B
Problem Solving & Reasoning
Use substitution to solve these multi-step problems and explain your reasoning.
1.
The sum of two numbers x and y is 12. If x=2y, find the values of x and y.
[4 marks]2.
A rectangle has length l=3w and width w. If the perimeter is 48 units, find the values of l and w.
[4 marks]3.
A mixture of coffee and milk weighs 10 kg. If coffee is x kg and milk is y kg, and x=2y, find the individual weights.
[4 marks]C
Real-world Applications
Solve these real-life problems involving multiple variables using substitution.
1.
A garden has x meters of fencing along one side and y meters along the other. If the total fencing used is 30 meters and x=2y, find the lengths of x and y.
[4 marks]2.
Two tanks are filled with water. Tank A has x liters, and Tank B has y liters. If total water is 100 liters and x=3y, find the volumes of each tank.
[4 marks]D
Challenge & Extension
Tackle these more challenging problems involving multiple variables and substitution.
1.
Solve for x and y given the system: 2x + y = 10 and x = y + 3. Find the values of x and y.
[3 marks]2.
A chemist mixes x grams of substance A and y grams of substance B. If x=2y and the total weight is 36 grams, find the individual weights of each.
[3 marks]E
Mixed Review
Answer these questions that test your understanding of multiple variables and substitution.
1.
Evaluate 5x - 2y when x=4 and y=3.
[2 marks]2.
If x=1, y=4, and z=2, evaluate 3x + 2y + z.
[2 marks]3.
Using the system: x= y + 2, y= 3, find x.
[2 marks]F
Error Analysis
The following problem is frequently answered incorrectly. Identify the mistake and correct it.
1.
A student substitutes x=3 into the equation 2x + y = 10 and finds y=4. Identify the mistake and provide the correct value of y.
[3 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
- • Change grade level (Grade 6 → Grade 7)
- • Swap topics (Harry Potter → Macbeth)
- • Add more questions (10 → 15)
- • Adjust difficulty
Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet