What is the greatest number of pieces you can buy for exactly Rs 50/-?

Question

You can buy 4 chocolates bars and 3 ice cream cones for Rs 50/- and 3 chocolates bars and 4 ice cream cones for Rs 48/-.
What is the greatest number of pieces you can buy for exactly Rs 50/-?

Answer 1

8

---

chocolates- x
ice cream cones- y
4x+3y=50 ------> (1)
3x+4y=48 ------> (2)
(1)-(2) => x-y=2 => y=x-2 then (1) = 4x+3x-6=50 => x=8, y=6
The greatest number will be achieved with as much of possible Rs 6 which is the combination of 1x8+7x6=50, so the number is 1+7=8

Answer 2

Let the price of 1 chocolate be x and that of 1 cone be y
4x + 3y = 50
3x + 4y = 48
Adding these, we get 7x + 7y = 98 or x + y = 14
Subtracting these, we get x - y = 2

Now adding these 2 equations, we get 2x = 16, or x = 8
Substituting in either equation, we get y = 6

The price of 1 chocolate is 8 and that of 1 cone is 6
Hence we can buy 7 cones (Rs 42) and 1 chocolate (Rs 8)
Therefore, in Rs 50 we can buy 8 pieces.