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Real-life and equivalent expressions

الأسبوع 7 · المقادير الجبرية في الحياة والمقادير المتكافئة · 3 دروس
1

Using algebraic expressions in real-life stories

Discover Mathematics P6: Term 1, Unit 3, Lessons 6–7
GoalWrite and evaluate expressions for real situations and say what each part means.
New words
fixed amount · a cost that stays the same, like a starting feerate · the cost for each one, like 3 LE for each kmformula · an expression that works out a quantity for any value of the letter
Explanation

Many real prices follow a pattern: a fixed amount plus a rate times a number. A taxi charges 8 LE to start and 3 LE for each kilometre, so a trip of k km costs 8 + 3k LE. The term 3k is the cost of the distance, and 8 is the fixed starting fee. To use the formula we substitute: for k = 6, the cost is 8 + 3 × 6 = 8 + 18 = 26 LE. Always read the answer back in the story: “A 6 km trip costs 26 LE.” With two kinds of things we use two letters: if adult tickets cost 20 LE and child tickets cost 10 LE, then a adults and c children pay 20a + 10c.

Part of 8 + 3kMeaning
8fixed starting fee (LE)
3k3 LE for each of the k kilometres
8 + 3ktotal cost of the trip
Worked examples
k1246
8 + 3k (LE)11142026
Taxi: 8 + 3k. A 1 km trip costs 11 LE, 2 km costs 14 LE, 4 km costs 20 LE and 6 km costs 26 LE.
n135
12n + 30426690
School shop: n notebooks at 12 LE each plus a bag for 30 LE cost 12n + 30. For n = 5: 12 × 5 + 30 = 60 + 30 = 90 LE.
GroupAdults aChildren cCost (LE)
Family2370
Train tickets: adults 20 LE, children 10 LE. a adults and c children pay 20a + 10c. For 2 adults and 3 children: 20 × 2 + 10 × 3 = 40 + 30 = 70 LE.
Class activity

Shop formula. Pretend your home is a shop that sells fruit. Choose a price per kilogram and a fixed bag fee. Write the formula for k kilograms. A grown-up orders different weights and you work out each bill, writing every step.

Practice
1
Use the taxi formula 8 + 3k to find the cost of a 10 km trip.
2
Use 12n + 30 to find the cost of 3 notebooks and a bag.
3
In 12n + 30, what does the number 12 stand for?
4
The perimeter of a rectangle is 2l + 2w. Find it when l = 9 cm and w = 4 cm.
5
A phone plan costs 50 LE a month plus 0.5 LE for each message m. Write the formula and find the bill for 40 messages.