100 Apples
Algebra
Level
3
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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1 solution
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