Abhishek had a certain number of Re1 coins, Rs 2 coins and Rs 10 coins. Ifthe number of Re 1 coins he had is six times the number of Rs 2 coins Abhishekhad, and the total worth of his coins is Rs 160, find the maximum number of Rs10 coins Abhishek could have had.
Question
Abhishek had a certain number of Re1 coins, Rs 2 coins and Rs 10 coins. Ifthe number of Re 1 coins he had is six times the number of Rs 2 coins Abhishekhad, and the total worth of his coins is Rs 160, find the maximum number of Rs10 coins Abhishek could have had.
Solution
Let's denote:
- The number of Re 1 coins as x
- The number of Rs 2 coins as y
- The number of Rs 10 coins as z
From the problem, we know that:
- x = 6y (The number of Re 1 coins is six times the number of Rs 2 coins)
- x + 2y + 10z = 160 (The total worth of his coins is Rs 160)
We can substitute equation 1 into equation 2:
6y + 2y + 10z = 160 8y + 10z = 160 4y + 5z = 80
Since y and z must be integers (as they represent the number of coins), we can start by setting y = 1 and solve for z:
4(1) + 5z = 80 5z = 76 z = 76/5 = 15.2
Since z must be an integer, we can't have y = 1. Let's try y = 2:
4(2) + 5z = 80 5z = 72 z = 72/5 = 14.4
Again, z is not an integer. We continue this process until we find an integer value for z. If we set y = 4, we get:
4(4) + 5z = 80 5z = 64 z = 64/5 = 12.8
Still not an integer. If we set y = 5, we get:
4(5) + 5z = 80 5z = 60 z = 60/5 = 12
So, the maximum number of Rs 10 coins Abhishek could have had is 12.
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