Radha stops at a fruit cart. The price tags say that mangoes cost ₹60 per kg and bananas cost ₹50 per kg. She buys some kilograms of mangoes and some kilograms of bananas. Altogether, she pays ₹280. Can we express this situation as an equation?
Step-by-step solution
To find: An equation that describes Radha’s purchase
Idea: We do not know either quantity, so we give each unknown its own letter. Cost = rate × quantity for each fruit, and the two costs add up to the total bill.
- Two quantities are unknown, so use two letters: let x = number of kilograms of mangoes and y = number of kilograms of bananas.½ mark
- Cost of mangoes = 60 × x = ₹60x. Cost of bananas = 50 × y = ₹50y.½ mark
- The two costs together make the total bill of ₹280, so 60x + 50y = 280.½ mark
- Both sides stand for the same quantity, the total cost in rupees. The equation has two variables, each with power 1, so it is a linear equation in two variables.½ mark
Check: If Radha bought 3 kg of mangoes and 2 kg of bananas: 60 × 3 + 50 × 2 = 180 + 100 = 280 ✓. So (x, y) = (3, 2) fits the equation.
Answer to write in the exam
Let mangoes bought = x kg and bananas bought = y kg
Cost of mangoes = ₹60x, cost of bananas = ₹50y
Total cost = ₹280
∴ 60x + 50y = 280
Common mistakes that cost marks
- Writing 60 + 50 = 280 or x + y = 280: the rates must multiply the quantities, and the total is in rupees, not kilograms.
- Swapping the rates, as in 50x + 60y = 280 when x stands for mangoes. Each rate must go with its own fruit.
- Using one letter for both fruits. The two quantities can be different, so they need two different variables.
How this can come in the exam
Pens cost ₹12 each and pencils ₹5 each. Arun buys p pens and q pencils for ₹94. The equation is
- 12q + 5p = 94
- 12p + 5q = 94
- p + q = 94
- 17(p + q) = 94
Show answer
(B) 12p + 5q = 94
Cost of pens = 12p, cost of pencils = 5q; together 12p + 5q = 94.
A school buys chairs at ₹450 each and tables at ₹900 each and spends ₹13,500 in all. Write this as a linear equation in two variables and give one possible solution.
Show answer
Let x = chairs, y = tables: 450x + 900y = 13500, i.e. x + 2y = 30 (1 mark). One solution: x = 10, y = 10, since 4500 + 9000 = 13500 (1 mark).Try one yourself
Apples cost ₹120 per kg and grapes ₹80 per kg. Neha pays ₹440 for some of each. Write an equation for this.
Show answer
Let x kg of apples and y kg of grapes: 120x + 80y = 440 (or 3x + 2y = 11 after dividing by 40).
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