Fungai steps into the supermarket to buy a candle. A candle costs 29 cents. She has a $2 note, and the shopkeeper has 5 cent and 6 cent coins only in his till. If Fungai is to get her change in these denominations,
what is the largest product she can obtain after multiplying the number of 5 cent coins by the number of 6 cent coins in her change?
The solution starts with the equation 6x + 5y = 171. Where did they get 171
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If she buys just one candle, then remaining is 200 cents - 29 cents = 171 cents
her change (1.71) consists of how many (.06) and how many (.05)?
Do u hv the answer???
Is it 15 coins of 5 cents and 16 coins of 6 cents
their product is 15 x 16 =240
Is my suggested answer right???
Yes you are right Harkirat
6s + 5f = 171
M = sf ; f= (-6s +171)/5
M = s[(-6s +171)/5]
M = (-6s^2 +171s)/5
M' = (-12s +171)/5
M' = 0 when s = 171/12 = 14.25; so its close to that
when six cent = 14 or 15 looks to be the options; and Hark decided that fate :)
My logic goes as follows:
one 5 cent coin and one 6 cent coin together make 11 cents
If we divided 171 by 11, we get Quotient as 15 and remainder is 6
This means that if she gets 15 coins of 5 cents and 15 coins of 6 cents then remainder is 6 cents
So we can say that if she has 15 coins of 5 cents it is = 75 cents
and 15 + 1 coins of 6 cents ie 16 coins of 6 cents it is = 96 cents
75 + 96 = 171
so product of number of coins is 15 x 16 = 240
Hope it explains how I arrived at the solution......!!!