# too big for up here?

a certain number decreased by 4 is equal to 8 increased by the quotient of the same number and 5. what is the number?

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• JasonM
Lv 7

Let x be the number.

Then x - 4 = 8 + x/5

If x = 15, then we have 15 - 4 = 8 + 3, which is true since both sides would equal 11.

So, x =15 is such a number.

the number is 15. 15-4 = 11 15/5= 3+8=11

Call this certain number 'n' (I would think it would be better to call it an 'uncertain' number at this moment).

The certain number decreased by four: n - 4,

The quotient of the certain number and five: n ÷ 5,

Eight increased by that quotient: 8 + n/5.

Set these equal:

n - 4 = 8 + n/5

n - 4 = 8 + n/5,

multiply both sides by 5:

5n - 20 = 40 + n,

5n =60 + n,

subtract 'n' from both sides:

4n = 60,

divide both sides by 4:

n = 15

voilà!

let x equal the number

certain number decreased by 4 is the same as x-4

8 increased by the quotient of the same number and 5 is the same as 8+(x/5)

set the two equations equal.... x-4=8+(x/5)

get both x's on the right side by subtracting...

-4=8+(x/5)-x

subtract 8 from the right side...

-12=(x/5)-x

now to subtract, find the common denominator (5) for (x/5)-x...

-12=(x/5)-(5x/5)

multiply by 5 on both sides to eliminate the fraction...

-60=x-5x

subtract the like terms...

-60=-4x

finally, divide to get x alone...

x=15

another way, if you have a graphing calculator, is to put each side of the equation into Y= (put the left side in Y1 and the right in Y2) and graph. then, you can find the intersection, and the x-coordinate will be your final answer!

thanks for distracting me from my own math homework...

Source(s): me and math experiance

Make an equation based on the word problem (and always remember to look for negative answers, although in this case there are none).

The equation is as follows:

x - 4 = 8 + x/5

First add 4 to both sides yielding

x = 12 + x/5

Second, subtract x/5 from both sides to get your variable on one side of the equation:

x - x/5 = 12

Remember that x and 5x/5 are equivalent. Understanding this will make the next step easier

5x/5 - x/5 = (5x - x)/5 = 4x/5 = 12

Now multiply both sides by 5

4x = 60

then divide by 4

x = 15

And there you have it.

x-4=8+(x/5)

15-4=11

8+3=11