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A man buys some shirts and some ties. Shirts cost Tk. 7 each and the ties cost Tk. 30 each. If the man spends exactly Tk. 810 and buys the maximum number of shirts possible under these conditions, what is the ratio of shirts to ties?

A man buys some shirts and some ties. Shirts cost Tk. 7 each and the ties cost Tk. 30 each. If the man spends exactly Tk. 810 and buys the maximum number of shirts possible under these conditions, what is the ratio of shirts to ties? Correct Answer 3 : 2

We can create the equation: 7S + 3T = 81 or,7S = 81 - 3T or,7S = 3(27 - T) or,S = 3(27 - T)/7 The greatest value of S will be obtained when T is as small as possible. The smallest value of T which produces a number divisible by 7 after substitution is 6, so when T is 6 we have: S = 3(21)/7 = 9 So, the ratio of S to T is 9 : 6 = 3 : 2.

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