Lesson 8 of 10 · 7 min
Word problems: budgets, marks and consecutive numbers
NCERT §5.3
The stall is set up. Now Riya wants to know how many glasses of juice she must sell to make it worthwhile, and her classmates bring their own puzzles about marks and numbers.
The lesson in notes
In short
Turn the words into an inequality: 'at most' gives ≤, 'at least' gives ≥, 'more than' gives >, and 'less than' gives <.
Budget: fruit cartons cost ₹45 and the budget is ₹500, so 45x ≤ 500, x ≤ 100/9 ≈ 11.1, and at most 11 cartons can be bought.
Profit: juice sells at ₹15 a glass and the stall costs ₹200 to run. For a profit of at least ₹400, 15x − 200 ≥ 400, so 15x ≥ 600 and x ≥ 40 glasses.
Marks: a student scored 68 and 81 in two tests and wants an average of at least 75 over three. Then (68 + 81 + x)/3 ≥ 75, so 149 + x ≥ 225 and x ≥ 76.
Consecutive numbers: find consecutive even positive integers, both greater than 6, whose sum is less than 30. With x and x + 2: x > 6 and 2x + 2 < 30, so 6 < x < 14. The even values are 8, 10 and 12, giving the pairs (8, 10), (10, 12) and (12, 14).
Always check the answer against the story: counts must be whole numbers, marks cannot exceed the maximum, and both members of a pair must satisfy every condition.