🧠 Question:
Raju has $10. If he buys 8 pears and 5 mangoes, he will be short of $1.10. If he buys 5 pears and 4 mangoes, he will receive $1.75 in change. Find the price of each fruit.
📘 Solution:
Let price of pear = x
Let price of mango = y
From first condition:
Total money needed = 10 + 1.10 = 11.10
8x + 5y = 11.10 ...(1)
From second condition:
Money spent = 10 - 1.75 = 8.25
5x + 4y = 8.25 ...(2)
Multiply (2) by 5:
25x + 20y = 41.25 ...(3)
Multiply (1) by 4:
32x + 20y = 44.40 ...(4)
Subtract (3) from (4):
7x = 3.15
x = 0.45
Put x in (2):
5(0.45) + 4y = 8.25
2.25 + 4y = 8.25
4y = 6
y = 1.50
✅ Price of pear = $0.45
✅ Price of mango = $1.50
