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Applications of Simple Equations to Practical Situations

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Example

The sum of three times a number and 11 is 32. Find the number.

If the unknown number is taken to be x, then three times the number is 3x and the sum of 3x and 11 is 32.

That is, 3x + 11 = 32.

3x = 32 – 11
3x = 21

Now, divide both sides by 3

So, x = `21/3` = 7

The required number is 7.

Example

Raju’s father’s age is 5 years more than three times Raju’s age. Find Raju’s age, if his father is 44 years old.

The equation that gives Raju's age is 3y + 5 = 44
we first transpose 5, we get
3y
= 44 – 5 = 39
Dividing both sides by 3, we get,
y
= 13
That is, Raju’s age is 13 years.

Example

Find a number, such that one-fourth of the number is 3 more than 7.

Let us take the unknown number to be y; one-fourth of y is `y/4`.

This number `y/4` is more than 7 by 3.

Hence we get the equation for y as `y/4 – 7 = 3`.

To solve this equation, first transpose 7 to RHS We get,

`y/4 = 3 + 7 = 10`.

We then multiply both sides of the equation by 4, to get

`y/4 xx 4 = 10 xx 4`

y = 40........(the required number)

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