# 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?

Relevance

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