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Question P5–P6 The equal concept

Files and pens — the cost of 1 pen

The total cost of 2 identical files and 1 pen is $19.05. The total cost of 3 such files and 5 such pens is $44.50. Find the cost of 1 pen.

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Answer

1 pen costs $4.55.

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About this method

The equal concept

The question tells you a part of one pile equals a part of another.

In this one. Multiply each purchase until the item you do not want appears the same number of times in both — then the difference between the two totals is made of the wanted item alone.

the two shaded parts are the same sizePile Aa third of APile Ba fifth of B

How to spot it

Two different groups each get their own fraction or percentage, and the question links them with 'the same as', 'twice as many as', or a shared cost across different units.

Common mistake

Children compare the two fractions without first relating them to a common whole. A smaller fraction of a larger group can be bigger than a larger fraction of a smaller group.

Practise a similar question

Standard 3/5 of a box of red marbles equals 2/3 of a box of blue marbles. The box of red marbles contains 30 marbles. How many blue marbles are there?
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