Help! Word problems.

Question

A number, one-fifth of that number, and one-third of that number are added. The result is 69. What is the original number?

Answer 1

Let x be the number.

From the first 2 sentences, we have:

x + x/5 + x/3 = 69

LCD is 15, so multiply by both sides:

15x + 3x + 5x = 1035

23x = 1035, x = 45 <<fixed a careless error>>

BUT--another interpretation of the wording: 1/3 of "that number" may mean the preceding number. If so:

x + x/5 + x/15 = 69

15x + 3x + x = 1035

19x = 1035. x = 54.47

Answer 2

Let the number be x.

"A number, one-fifth of that number, and one-third of that number are added. The result is 69."

x + (1/5)x + (1/3)x = 69

To get rid of the denominators, multiply by the LCM of 3 and 5 ---- 15.

15x + 3x + 5x = 1035

23x = 1035 [collect like terms]

x = 45 [divide both sides by 12]

Checking (very impotant):

Is 45 + (1/5)45 + (1/3)45 = 69 ?

45 + 9 + 15 = 69 ?

69 = 69 ?yes



Answer 3

Let's call the number we're looking for x. Then, a third of x is x/3. A fifth of x is x/5, and we can write the equation

x+x/3 +x/5 = 69.

Then we just need to get a common denominator on the left to add all those fractions. The common denominator is 15, and if you need to know how to get common denominators, please look on Khan Academy or get in touch. With a common denominator of 15, our equation becomes

15x/15 + 5x/15 + 3x/15 = 69

or

(15x+5x+3x)/15=69

which simplifies to

23x/15=69.

Multiply both sides by 15 to get

23x=1035

And divide both sides by 23 to get

x=45.

To check, put 45 back into the original situation and see if it works. A third of 45 is 15. A fifth of 45 is 9.

15+9+45=69, so we're good!

Happy mathing!