7.3.2

Combining Two Variables

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Problem Solving with Two Variables

When you’re given a statement, you can use algebra to find different options that the answers can be.

Possible answers

Possible answers

  • 12 + 12 = 24
  • 13 + 11 = 24
  • 14 + 10 = 24
  • 15 + 9 = 24
    • There are multiple correct answers, so you need to find all the different combinations available to answer the question fully.
What could the answers be?

What could the answers be?

  • 36 and 30
  • 35 and 29
  • 34 and 28
  • 33 and 27
  • 32 and 26

Problem Solving with Two Variables

When you’re given a statement, you can use algebra to find different options that the answers can be. You can be given these statements numerically (using numbers).

Example 1

Example 1

  • This numerical statement means:
    • The difference between the two numbers (a and b) is 23.
    • One of the numbers (a) must be less than 37.
    • One of the numbers (b) must be bigger than 9.
Possible answers

Possible answers

  • 33 and 10
  • 34 and 11
  • 35 and 12
  • 36 and 13
What could the answers be?

What could the answers be?

  • 36 and 30
  • 35 and 29
  • 34 and 28
  • 33 and 27
  • 32 and 26
Jump to other topics
1

Year 5 - Number

1.1

Number & Place Value

1.1.1The Value of Digits to Millions1.1.2Smallest & Biggest Numbers to Millions1.1.3Ordering Numbers to Millions1.1.4Counting in Powers of 101.1.5Counting in Negative Numbers1.1.6Rounding Numbers up to 1,000,0001.1.7Reading Roman Numerals
1.2

Addition & Subtraction

1.2.1Written Methods for Adding Large Numbers1.2.2Written Methods for Subtracting Large Numbers1.2.3Mental Addition & Subtraction1.2.4Rounding to Check Your Answer
1.3

Multiplication & Division

1.3.1Multiples1.3.2Factors1.3.3Prime Numbers1.3.4Prime Factors1.3.5Composite Numbers1.3.6Factor Trees1.3.7Multiplication by a 1 Digit Number1.3.8Long Multiplication Using Column Method1.3.9Times Tables1.3.10Division1.3.11Multiplying & Dividing by 10, 100 & 1,0001.3.12Square & Cube Numbers
1.4

Fractions & Decimals

1.4.1Compare & Order Fractions1.4.2Identifying Equivalent Fractions1.4.3Add & Subtract Fractions1.4.4Mixed Numbers & Improper Fractions1.4.5Multiplying Fractions by Whole Numbers1.4.6Converting Between Decimals & Fractions1.4.7Rounding Decimals1.4.8Ordering Decimals
2

Year 5 - Measurement

2.1

Measures

2.1.1Metric Measurements2.1.2Imperial Measurements
2.2

Perimeter & Area

2.2.1Perimeter2.2.2Area
2.3

Time

2.3.1Units of Time
3

Year 5 - Geometry

3.1

Properties of 3D Shapes

3.1.1Types of 3D Shapes3.1.2Faces, Edges & Vertices
3.2

Properties of 2D Shapes

3.2.1Polygons
3.3

Angles

3.3.1Angles in Degrees3.3.2Types of Angle3.3.3Finding Missing Angles
3.4

Position & Direction

3.4.1Reflection & Translation
4

Year 5 - Statistics

4.1

Graphs

4.1.1Line Graphs4.1.2Tables4.1.3Timetables
5

Year 6 - Number

5.1

Number & Place Value

5.1.1The Value of Digits to Ten Millions5.1.2Ordering Numbers to Millions5.1.3Rounding5.1.4Negative Numbers
5.2

Multiplication & Division

5.2.1Multiplication by a 2 Digit Number5.2.2Division5.2.3Multiples5.2.4Factors5.2.5Primes
5.3

Mental Maths

5.3.1Multiplying & Dividing by 10, 100 & 1,0005.3.2Addition & Subtraction5.3.3Adding & Subtracting 10, 100 & 1,0005.3.4Multiplication & Division
5.4

Order of Operations

5.4.1BIDMAS
5.5

Problem Solving

5.5.1Addition & Subtraction Multi-step Problems5.5.2Problem Solving with Proportion
5.6

Fractions & Decimals

5.6.1Simplifying Fractions Using Equivalents5.6.2Ordering Different Types of Fraction5.6.3Adding & Subtracting Fractions5.6.4Adding & Subtracting Mixed Numbers5.6.5Multiplying Fractions5.6.6Dividing Fractions by Whole Numbers5.6.7Converting Between Decimals & Fractions5.6.8Dividing Decimals
6

Year 6 - Ratio & Proportion

6.1

Ratio

6.1.1Using Ratios6.1.2Simplifying Ratios
6.2

Percentages

6.2.1Calculating Percentages
6.3

Scale

6.3.1Scale of 2D Shapes
7

Year 6 - Algebra

7.1

Sequences

7.1.1Describing Sequences7.1.2Finding Gaps in Sequences
7.2

Missing Number Problems

7.2.1Missing Number Problems
7.3

Equations

7.3.1Balancing Equations7.3.2Combining Two Variables
8

Year 6 - Measurement

8.1

Problem Solving

8.1.1Problem Solving with Measures
8.2

Unit Conversion

8.2.1Conversion Between Miles & Kilometres
8.3

Perimeter, Area & Volume

8.3.1Area8.3.2Volume8.3.3Nets8.3.4Faces, Edges & Vertices
8.4

Angles

8.4.1Types of Angle8.4.2Finding Missing Angles8.4.3Finding Missing Angles in Triangles8.4.4Vertically Opposite Angles
8.5

Circles

8.5.1Parts of a Circle
8.6

Coordinate Grids

8.6.1Positions on Coordinate Grids8.6.2Reflection & Translation
9

Year 6 - Statistics

9.1

Displaying Data

9.1.1Pie Charts9.1.2Line Graphs
9.2

Averages

9.2.1Mean

Practice questions on Combining Two Variables

Can you answer these? Test yourself with free interactive practice on Seneca — used by over 10 million students.

  1. 1
    Which pair of numbers is NOT an answer to the following question:<br>__The difference between two numbers is 3. The two numbers are between 45 and 55.__Multiple choice
  2. 2
    Which pair of numbers is NOT an answer to the following question:<br>__The difference between two numbers is 7. The two numbers are between 12 and 29.__Multiple choice
  3. 3
    Which pair of numbers is NOT an answer to the following question<br>__The sum of two numbers is 33. The two numbers are between 10 and 20.__Multiple choice
  4. 4
    Which pair of numbers is NOT an answer to the following question<br>__The sum of two different numbers is 12. The two numbers are below 10.__Multiple choice
  5. 5
    Which pairs of numbers is NOT the answer to the following question:<br>__a &minus; b = 15<br>a < 61<br>b > 42__Multiple choice
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Balancing Equations

Problem Solving with Measures