Senior 3 • Simultaneous Equations • Showcase mission

The Canteen Receipt Mystery

Two canteen receipts have totals but no item prices. Recover the price of one samosa and one juice before tomorrow’s order is placed.

⏱ 60–75 minutes✎ Pencil and paper★ Explain every answer

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YOUR MISSION PROGRESS • 0 OF 15 PRACTICE QUESTIONS SOLVED0%

The situation

Two unknown prices are hiding in two receipts.

Receipt A shows 2 samosas and 3 juices for UGX 8,000. Receipt B shows 3 samosas and 2 juices for UGX 8,500. The price list has gone missing, but both receipts were calculated correctly.

⚠ THE PROBLEM YOU MUST SOLVE

What does one samosa cost, and what does one juice cost?

Your job: turn both receipts into equations, eliminate one unknown, find both prices, and verify them in the original receipts.

Foundation • Two clues for two unknowns

An equation is a true statement about the receipt.

Let s be the price of one samosa and j be the price of one juice. Each receipt becomes an equation. Because the same prices appear in both receipts, the equations must be solved together.

RECEIPT A

2s + 3j = 8,000

Two samosa prices plus three juice prices must equal the first total.

RECEIPT B

3s + 2j = 8,500

Three samosa prices plus two juice prices must equal the second total.

THE GOAL

Make one unknown disappear

Multiply the equations so one variable has matching coefficients, then subtract.

Worked example • Follow the reasoning

Eliminate j and uncover the prices.

Multiply Receipt A by 2 and Receipt B by 3. Both equations will contain 6j.

SCALE BOTH EQUATIONS4s + 6j = 16,000; 9s + 6j = 25,500

Multiplying every term keeps each equation balanced.

SUBTRACT5s = 9,500 → s = 1,900

The 6j terms cancel, leaving the samosa price.

SUBSTITUTE AND CHECK2(1,900) + 3j = 8,000 → j = 1,400

Receipt B also gives 3(1,900) + 2(1,400) = 8,500.

QUICK CHECK 1

Which equation represents Receipt A?

QUICK CHECK 2

If 5s = 9,500, what is s?

QUICK CHECK 3

Use s = 1,900 in 2s + 3j = 8,000. What is j?

QUICK CHECK 4

Solve x + y = 10 and x − y = 2.

QUICK CHECK 5

Solve 2x + y = 11 and x + y = 7.

QUICK CHECK 6

If x=3 in x + 2y = 11, what is y?

QUICK CHECK 7

Does (x,y)=(2,3) solve x+y=5 and 2x−y=1?

QUICK CHECK 8

What happens with x+y=4 and 2x+2y=10?

QUICK CHECK 9

What happens with x+y=4 and 2x+2y=8?

QUICK CHECK 10

To eliminate x from x+2y=7 and 3x−y=8, what can you do first?

QUICK CHECK 11

Adding x+y=9 and x−y=1 gives which equation?

QUICK CHECK 12

Two pens and one book cost UGX 7,000. Which equation fits?

QUICK CHECK 13

Check Receipt B using s=1,900 and j=1,400.

QUICK CHECK 14

If a=4 and b=2, what is 3a+2b?

QUICK CHECK 15

On a graph, what represents the solution to two simultaneous linear equations?

Final scenario challenge

How much should tomorrow’s order cost?

The canteen orders 4 samosas and 5 juices at the recovered prices. Choose the verified total.

Explain your thinking

Why must the two equations describe the same item prices?

Write two or three sentences. Use the mathematical steps from the mission as evidence—not only the final answer.

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Workbook and teaching support

Continue on paper, teach it in class, or send the guided activity home.

STUDENT PDF

Mission Workbook

Foundation notes, guided practice, final scenario and reflection.

Download workbook ↓TEACHER / PARENT PDF

Teaching Guide

Lesson flow, support prompts, misconceptions and complete answers.

Download guide ↓

Senior 3 SHOWCASE MISSION

You made the mathematics visible.

A strong answer does not guess. It represents, calculates and explains.

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