Three fruits
Quince, quonce and quance are three types of fruit. Can you work out the order of heaviness of the fruits?
Age
14 to 16
Challenge level
Problem
Quince, quonce, and quance are three types of fruit.
7 quince weigh the same as 4 quance.
5 quance weigh the same as 6 quonce.
Put the fruit into order of weight, heaviest last.
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If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Ans: Quince, quonce, quance
7 quince weigh the same as 4 quance, so a quince weighs less than a quance. [1]
5 quance weigh the same as 6 quonce, so a quonce weighs less than a quance. [2]
So quance are the heaviest.
20 quance must weigh the same as 35 quince. (from [1])
20 quance must weigh the same as 24 quonce (from [2])
So 35 quince weigh the same as 24 quonce, so a quonce weighs more than a quince.
So quince is the lightest, and quance is the heaviest.