Class 9 · Mathematics and money
Compare mobile data plans with equations
Plan A costs more each month but less per GB. Plan B is cheap to start but costs more per GB. Which is better for you?
What you will learn: Model plans as linear equations and find the break-even point.
Small test at the end: scroll down to the end of this page for five short questions that check what you have learnt. Tap an answer, then press Check answer. Go to the questions ↓
Jump to: Check yourself · For grown-ups · For teachers
Safety first
Made-up plans only.
Keep it safe:
- Use made-up plans. Do not share anyone's phone number or bills.
You will need
- Graph paper
- A pencil and ruler
- Made-up plan pricesUse the ones on this page or invent your own.
Time: About 45 minutes.
The story
Tara needs a mobile data plan. Plan A costs more each month but less for each GB. Plan B is cheap to start but costs more for each GB. "Just take the cheap one," says Tanmay. Dhruv asks, "Cheap for how many GB?" How could an equation show which plan is better for her?
The idea
A plan with a fixed charge F and a cost c for each GB costs C = F + c × g, where g is the number of GB used.
Plan A: C = 100 + 10g. Plan B: C = 40 + 20g. Each is a linear equation, so its graph is a straight line.
The break-even point is where the two plans cost the same. Set them equal: 100 + 10g = 40 + 20g, so 60 = 10g and g = 6.
Below 6 GB, Plan B is cheaper (lower fixed charge). Above 6 GB, Plan A is cheaper (lower cost per GB).
Worked example
Finding the break-even point
- Plan A: 100 + 10g. Plan B: 40 + 20g.
- Set equal: 100 + 10g = 40 + 20g.
- Take 40 and 10g from both sides: 60 = 10g, so g = 6.
- Check: A = 100 + 60 = ₹160; B = 40 + 120 = ₹160.
Both plans cost ₹160 at 6 GB. Use less than 6 GB a month and Plan B is cheaper; more, and Plan A is.
Try it
Write the equations.
C = F + c × g for each plan.
Make a table.
Cost of each plan at 0, 2, 4, 6, 8 and 10 GB.
Draw the graph.
GB along the bottom, cost up the side, one line per plan.
Find the break-even point.
Where the lines cross. Check it by solving the equations.
Advise.
Write which plan suits someone who uses 3 GB, and someone who uses 9 GB.
What you make (paper or offline)
Your plan comparison
A table of costs.
A graph with both lines and the break-even point marked.
Advice for a light user and a heavy user.
Make it on paper. Keep it with you. Nothing to upload.
Check yourself
Five questions about what this page teaches. Choose an answer and press Check answer, or open "See the answer and why". Nothing is saved or sent: your choices stay on this screen and disappear when you leave or reload the page.
How do you want to answer? You choose, and you can change at any time.
See the answer and why
- A. ₹120 Not this one. ₹120 is what Plan B costs at 4 GB.
- B. ₹140 Correct. 100 + 10 × 4 = 140.
- C. ₹104 Not this one. Multiply 10 by 4 before adding: 100 + 40.
- D. ₹40 Not this one. That is only the per-GB part. Add the ₹100 fixed charge.
See the answer and why
- A. 10 GB Not this one. At 10 GB, A costs ₹200 and B costs ₹240.
- B. 4 GB Not this one. At 4 GB, A costs ₹140 and B costs ₹120.
- C. 6 GB Correct. 100 + 10g = 40 + 20g gives 60 = 10g, so g = 6.
- D. 3 GB Not this one. At 3 GB, A costs ₹130 and B costs ₹100.
See the answer and why
- A. Plan A, at ₹120 Not this one. Plan A costs ₹120, but Plan B costs less.
- B. Plan A, because its cost per GB is lower Not this one. For small use, the lower fixed charge of Plan B matters more.
- C. Plan B, at ₹80 Correct. 40 + 20 × 2 = 80, less than Plan A's 100 + 20 = 120.
- D. They cost the same Not this one. They cost the same only at 6 GB.
See the answer and why
- A. The total cost Not this one. That is C.
- B. The cost for each GB Not this one. That is c.
- C. The number of GB used Not this one. That is g.
- D. The fixed charge, paid even at 0 GB Correct. It is the starting cost before any data is used.
See the answer and why
- A. Plan A, because its cost rises only ₹10 per GB Correct. Its line is less steep, so it stays below Plan B after they cross.
- B. Neither: they cost the same at every amount Not this one. They cost the same only at 6 GB.
- C. Plan B, because its fixed charge is lower Not this one. The lower fixed charge helps only below 6 GB.
- D. Plan B, because it was cheaper at 2 GB Not this one. Being cheaper at 2 GB does not mean cheaper at 9 GB.
Think back
How much data does your family use? Which plan would suit it?
Why does the steeper line end up higher?
Investigate further
- Add Plan C: ₹200 with unlimited data. Where does it beat the others?
- Compare two auto-rickshaw fares with different starting charges.
For grown-upsTap a heading to open it. The safety notes are at the top of the page.
Before you start
- Graph paper. If you like, compare with real plan prices without sharing bills.
Questions that help
- "What do you pay even if you use nothing?"
- "Where do the lines cross, and what does that mean?"
What's really going on
Fixed charge plus rate is a linear model used everywhere: taxi fares, electricity, rent plus bills.
Break-even analysis helps people choose based on how much they really use.
Other ways to do it
- Compare two gym or tuition fee plans with a joining fee and a monthly fee.
For teachersLearning aims, classroom ideas and what to look for.
Learning aims
- Model costs with linear equations.
- Find and interpret a break-even point graphically and algebraically.
Subject links
- Mathematics: linear equations and graphs.
- Social science: consumer choices.
These links are general. They have not been checked against a specific board syllabus.
In the classroom
- Groups invent plans for other groups to compare.
What to look for
- Correct equations from words.
- Interprets the crossing point in context.