The difference of a number divided by 3 and 6 is equal to 5. What is the number?

4 Answers
Nov 5, 2017

The number is 30.

Explanation:

Let x be the number, then the equation is:

x/3-x/6 = 5x3x6=5

Multiply both sides of the equation by 6:

2x - x = 302xx=30

x = 30x=30

Nov 5, 2017

33

Explanation:

Let xx be the number

x/3 - 6 = 5x36=5

Multiplying both sides of the equation by 3,
x-18=15x18=15
x=15+18x=15+18

Therefore,
x=33x=33

Nov 5, 2017

See a solution process below:

Explanation:

First, let's call "a number": nn

Next, we can write "a number divided by 3" as:

n/3n3

Then, we can write "the difference between" a number divided by 3 "and 6" as:

n/3 - 6n36

Now, we can complete this equation by write "is equal to 5" as:

n/3 - 6 = 5n36=5

To solve this, first, add color(red)(6)6 to each side of the equation to isolate the nn term while keeping the equation balanced:

n/3 - 6 + color(red)(6) = 5 + color(red)(6)n36+6=5+6

n/3 - 0 = 11n30=11

n/3 = 11n3=11

Now, multiply each side of the equation by color(red)(3)3 to solve for nn while keeping the equation balanced:

color(red)(3) xx n/3 = color(red)(3) xx 113×n3=3×11

cancel(color(red)(3)) xx n/color(red)(cancel(color(black)(3))) = 33

n = 33

Nov 5, 2017

The number is either +33 or -3

Explanation:

color(red)("The difference of ")color(blue)("a number ")color(green)("divided by 3")color(red)(" and ")color(magenta)6color(brown)( " is equal to 5")

If we represent color(blue)("a number") by the variable color(blue)n

this becomes:
color(red)("The difference of ")color(blue)(n)color(green)(/3)color(red)(" and ")color(magenta)6color(brown)(=5)

This has two possible interpretations
{: (color(blue)(n)color(green)(/3) color(red)(-) color(magenta)6color(brown)(=5),color(white)("xx")"and"color(white)("xx"),color(magenta)6color(red)-color(blue)ncolor(green)(/3)color(brown)(=5)), (rarr color(blue)ncolor(green)(/3)=11,,rarrcolor(red)-color(blue)ncolor(green)(/3)color(brown)=-1), (rarr color(blue)n=33,,rarr color(blue)n=-3) :}