If three times a number is increased by 4, the result is the same as when five times a number is decreased by 20. What is the number?

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Answer 1 · 2016-11-08T13:56:05

The number, or $x$ $x$ as we chose to call it, is $12$ $12$ .

We will let the number we are looking for be represented by $x$ $x$ .

"the result is the same as" means this is an equation because each part of the stated problem is "the same" or equal.

For the first part of the equation (If three times a number is increased by 4):

"Three times a number" can be written as $3 X$ $3X$ .

"Is increased by 4" can then be written as $3 x + 4$ $3x + 4$ .

For the second part of the equation (when five times a number is decreased by 20.):

"When five times a number" can be written as $5 x$ $5x$ .

"Is decreased by 20" can then be written as $5 x - 20$ $5x - 20$ .

And because, as stated previous these two statements are equal we can solve for $x$ $x$ as follows while keeping the equation balanced:

$3 x + 4 = 5 x - 20$ $3x + 4 = 5x - 20$

$3 x + 4 - 3 x + 20 = 5 x - 20 - 3 x + 20$ $3x + 4 - 3x + 20 = 5x - 20 - 3x + 20$

$24 = 2 x$ $24 = 2x$

$\frac{24}{2} = \frac{2 x}{2}$ $24/2 = (2x)/2$

$x = 12$ $x = 12$