Red apples cost $5 each, yellow apples cost $1 each, and green apples cost $0.10 each. A man bought 100 apples and paid $100.

If he bought an odd number of red apples, then how many red apples did he buy?

The answer is 9.

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Red R

Yellow Y

Green G

R + Y + G = 100

5 R + 1 Y + 0.1 G =100

Three unknowns with two equations To make them 2 unknowns I will have to write the value of one of them

Red : number of possibilities of value = 19 (after excluding the value 20 which means all red)

Yellow : 99 (after excluding value 100)

Green : 9 (10,20,30,...)

So I will take the least possibilities which means that I will write value for Green apples

Starting from value 10

R+ Y + 10 = 100

5R + 1 Y + 1 = 100

Then R = 2.25 ( no fractions in apples so try the next possibility)

Untill I reach value 40

R + Y + 40 = 100

5 R + 1 Y + 4 = 100

R = 9

Y = 51

G = 40