Year 11 General Mathematics
Simultaneous Equations: Word Problems
Today is about turning a story into two equations, then solving them using substitution or elimination.
Start here
Word problems are not trying to hide the maths. They just make you find it first.
The goal is to pull out two unknowns and two facts. Once you have two equations, the solving part is the same as last lesson.
Two unknowns
Choose letters for the two things you need to find.
Two equations
Each useful fact in the problem should become one equation.
One answer pair
The answer has to work in both equations and in the story.
The word problem routine
| Step | What to write | What it does |
|---|---|---|
| Define the variables | x = ... and y = ... | Makes it clear what the letters stand for. |
| Write two equations | One equation for each useful fact. | Turns the story into algebra. |
| Choose a method | Substitution or elimination. | Pick the method that gives you the cleanest next line. |
| Solve | Find both unknowns. | Gives the ordered pair. |
| Answer the question | Write a sentence with units. | Makes sure the answer fits the original problem. |
Worked example
Example Tickets
Two adult tickets and one child ticket cost $47. One adult ticket and one child ticket cost $30. Find the cost of each ticket.
Define the variables:
Write the equations:
Choose a method: elimination is clean here because both equations have +c.
Subtract the equations:
Find the second value:
Answer: one adult ticket costs $17 and one child ticket costs $13.
Check the answer
Section A: write the equations
Do not solve these yet. Define the variables and write two equations.
A1. Tickets
Three adult tickets and two child tickets cost $82. One adult ticket and two child tickets cost $44.
Check equations
A2. Pens and notebooks
A student buys 12 items in total. Pens cost $3 each and notebooks cost $7 each. The total cost is $60.
Check equations
A3. Two numbers
Two numbers add to 31. The first number is 7 more than the second number.
Check equations
A4. Tables
A room has small tables and large tables. There are 14 tables in total. Small tables seat 4 people and large tables seat 6 people. The room seats 72 people.
Check equations
Section B: solve the equations
The equations have already been written. Choose substitution or elimination and solve.
B1
B2
B3
B4
B5
B6
Section B answers
- B1: (11, 7)
- B2: (5, 11)
- B3: (6.5, 6). This one has a decimal x-value, so take care.
- B4: (12, 7)
- B5: (7, 10)
- B6: (3, 11)
Section C: word problem practice
For each problem, define the variables, write two equations, solve, then answer in a sentence.
- Define the variables.
- Write two equations.
- Choose substitution or elimination.
- Write the final answer in words.
C1. Movie tickets
Two adult tickets and three child tickets cost $85. Two adult tickets and one child ticket cost $51. Find the cost of one adult ticket and one child ticket.
Check answer
C2. Stationery
A student buys 15 pens and notebooks altogether. Pens cost $2 each and notebooks cost $6 each. The total cost is $58. How many pens and notebooks did the student buy?
Check answer
C3. Tables
A hall has 18 tables. Small tables seat 4 people and large tables seat 6 people. Altogether, the tables seat 88 people. How many of each table are there?
Check answer
C4. Sandwiches and drinks
Three sandwiches and two drinks cost $39. One sandwich and two drinks cost $21. Find the cost of one sandwich and one drink.
Check answer
Practice simultaneous word problems
Change the options below to get a fresh set. Your working is saved only on this device.
Check answers for this set
Exit ticket
Complete this before the end of the lesson.
Write, solve and check
A school sells raffle tickets and drink vouchers. Four raffle tickets and one drink voucher cost $23. Two raffle tickets and one drink voucher cost $13. Find the cost of one raffle ticket and one drink voucher.