Question
Download Solution PDF8 apples and 10 oranges weigh 5 kg. 12 apples and 20 oranges weigh 9 kg. What is the weight (in kg, rounded off to the nearest integer) of 15 apples and 24 oranges?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
8 apples + 10 oranges = 5 kg
12 apples + 20 oranges = 9 kg
Let the weight of an apple be A kg and the weight of an orange be O kg.
Formula used:
We form two equations from the given information:
- 8A + 10O = 5
- 12A + 20O = 9
We need to find the weight of 15 apples and 24 oranges.
Calculation:
First, simplify the second equation:
12A + 20O = 9 ⇒ (Divide both sides by 2)
6A + 10O = 4.5
Now, subtract the second simplified equation from the first:
(8A + 10O) - (6A + 10O) = 5 - 4.5
⇒ 2A = 0.5
⇒ A = 0.25 kg
Substitute A = 0.25 in the first equation:
8(0.25) + 10O = 5
⇒ 2 + 10O = 5
⇒ 10O = 3
⇒ O = 0.3 kg
Now, calculate the weight of 15 apples and 24 oranges:
Weight = 15A + 24O
⇒ Weight = 15(0.25) + 24(0.3)
⇒ Weight = 3.75 + 7.2
⇒ Weight = 10.95 kg
∴ The weight of 15 apples and 24 oranges is approximately 11 kg.
Last updated on May 28, 2025
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