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Let us consider a problem that involves variables.
Madhu prepared some laddus and kept it in a tray. If \(10\) laddus are taken out, and still \(8\) laddus are remaining, find the number of laddus Madhu prepared?
Till now, the problems that we have solved are directly asked us to find the required things. But in this topic, we will be dealing with the English phrases and its equivalent mathematical notations to solve problems.
Let us go through some general keywords with its operations to translate the word problem to numerical form easily.
| Operation | Keywords | Example | Expression |
| Addition \((+)\) | add, sum, total, more than, added to, increased by, together, all together, combined, both, in all, join. | \(x\) is increased by \(y\). | \(x + y\) |
| Subtraction \((-)\) | subtract, minus, difference, less than, decreased by, fewer than, deduct, how much less/more/lesser, remaining, take away. | \(y\) fewer than \(x\). | \(x - y\) |
| Multiplication \((×)\) | multiply, of, product, times, twice(2 times), thrice (3times), doubled, by, at, sets of. | \(x\) is \(2\) times of \(y\). | \(x = 2y\) |
| Division \((÷)\) | quotient, ratio, over, per, divide, equal parts, for each, how many each, shared equally, share of, split. | ratio of \(x\) and \(y\). | \(x/y\) |
| Equal \((=)\) | equal to, is, same as, answer, gives, results in/as, are, yields. | The value of \(x\) results in \(5\). | \(x = 5\) |
Now we will solve the problem by splitting the phrases in it and understand its meaning.
Here, 'Madhu prepared some laddus and kept it in a tray'. The number of laddus Madhu prepared is unknown.
Then '\(10\) laddus are taken out'. \(10\) laddus were taken out from the unknown number of laddus prepared by Madhu. That is, \(10\) laddus need to be removed(subtracted) from the unknown number.
Now '\(8\) laddus are remaining' after subtracting \(10\) laddus.
Let the initial unknown number of laddus be '\(x\)'.
We have to remove(subtract) \(10\) laddus from the unknown number \(x\) gives the remaining \(8\) laddus.
\(x-10 = 8\)
\(x = 8+10\)
\(x = 18\).
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