Mathematics • Year 7 • Unit 2 • Lesson 11

Equations in the Real World

Turn everyday situations into equations — money saved, points scored, kids in a class — and check whether a given value is the solution by substitution.

Apply · Real-World Maths

1. Word problems

For each problem: choose a letter for the unknown, write an equation (with an = sign), and — if asked — check the given value by substitution. Show your LHS and RHS clearly.

1.1 — Birthday savings. Mia already had some money saved. Her grandmother gave her $25 and now Mia has $63.

(a) Let s be Mia's original savings (in dollars). Write an equation for the situation.
(b) Check whether s = 38 is the solution. 2 marks

Stuck? "Already had + $25 = $63" gives the equation. Don't try to solve it — just write it and substitute.

1.2 — Cinema tickets. A ticket costs $14. A group buys n tickets, plus a $7 booking fee, and the total bill is $63.

(a) Write an equation using n.
(b) Identify the LHS and the RHS.
(c) Check whether n = 4 is the solution. 3 marks

Stuck? "Cost per ticket × number of tickets" is 14n. Add the fee. Then check by substituting n = 4 into the LHS.

1.3 — Card game score. Sam scored 3 points for every red card he played, and finished on 21 points exactly.

(a) Let r be the number of red cards. Write an equation.
(b) Substitute r = 7 and show whether it is the solution. 2 marks

Stuck? "3 points per red card" gives 3r. The total is 21, so 3r = 21.

1.4 — Class lineup. A Year 7 class has b boys and 14 girls. There are 27 students in total.

(a) Write an equation for this situation.
(b) Check whether b = 13 is the solution by substitution. 2 marks

Stuck? "Boys + girls = total" gives b + 14 = 27.

1.5 — Pocket money. Lily is paid $8 per week plus a $5 bonus for finishing all her chores. One week she made $37.

(a) Use w for the number of weeks (assume the bonus is paid once). Write an equation.
(b) Identify the LHS and RHS.
(c) Check whether w = 4 is the solution. 3 marks

Stuck? "$8 per week × w weeks" is 8w. Add the $5 bonus. Total = $37 gives the equation.

2. Explain your thinking

This question is about communication, not just symbols. Use full sentences. 4 marks

2.1 A classmate writes: "5x + 2 is an equation because it has numbers and a letter." In your own words, explain (i) why 5x + 2 is NOT an equation, (ii) what would need to change to make it one, (iii) what the equals sign actually means in algebra (think balance scales), and (iv) what is the difference between solving an equation and just substituting a value to check it?

Stuck? Use the picture of a set of balance scales. The = sign is the pivot, not "the answer."

How did this worksheet feel?

Got it Partly Lost

What I'll revisit before next class:

Answers — Do not peek before attempting

1.1 — Birthday savings

(a) Equation: s + 25 = 63.
(b) Substitute s = 38: LHS = 38 + 25 = 63. RHS = 63. LHS = RHS ✓. Yes, s = 38 is the solution.

1.2 — Cinema tickets

(a) Equation: 14n + 7 = 63.
(b) LHS = 14n + 7; RHS = 63.
(c) Substitute n = 4: LHS = 14(4) + 7 = 56 + 7 = 63 = RHS ✓. Yes, n = 4 is the solution.

1.3 — Card game score

(a) Equation: 3r = 21.
(b) Substitute r = 7: LHS = 3(7) = 21 = RHS ✓. Yes, r = 7 is the solution.

1.4 — Class lineup

(a) Equation: b + 14 = 27.
(b) Substitute b = 13: LHS = 13 + 14 = 27 = RHS ✓. Yes, b = 13 is the solution (so there are 13 boys).

1.5 — Pocket money

(a) Equation: 8w + 5 = 37.
(b) LHS = 8w + 5; RHS = 37.
(c) Substitute w = 4: LHS = 8(4) + 5 = 32 + 5 = 37 = RHS ✓. Yes, w = 4 is the solution.

2.1 — Explain your thinking (sample response)

(i) 5x + 2 has no equals sign, so it makes no claim — it's just a phrase describing how to calculate something. There is nothing to "solve" because nothing is being said to be equal to anything.
(ii) To turn it into an equation, we need to add an equals sign and another value or expression. For example, 5x + 2 = 17 is an equation.
(iii) The equals sign means balance — the two sides have the same value, like the two pans of a set of scales. It does not mean "here comes the answer."
(iv) Solving an equation means finding the value(s) of the variable that make LHS = RHS — you don't yet know the answer. Substituting means you already have a value and you're checking whether it works.

Marking: 1 for the no-equals point; 1 for fixing it with =; 1 for the balance idea; 1 for the solve-vs-check distinction.