help with fractions and word problems

[Yvette Holloway]

Three people who work full time are to work together on a project, but their total time on the project is to be equivalent to that of only one person working full time. If one of the people is budgeted for 1/2 of his time to the project and a second person for 1/3 of her time, what part of the third worker's time should be budgeted to this project?

 

[rbcc]

I guess the one person who works full time would allocate 100% of their time to the project so the time that the three people working together put in would need to sum to 1

let x represent the amount of time persons 3 allocates to the project then write an equation to represent the total amount of time allocated to the project

1/2+1/3+x=1

do you know how to solve that?

 

[Yvette Holloway]

Response

I don't know how to solve for x....Please work the problem out for me!

I guess the one person who works full time would allocate 100% of their time to the project so the time that the three people working together put in would need to sum to 1

let x represent the amount of time persons 3 allocates to the project then write an equation to represent the total amount of time allocated to the project

1/2+1/3+x=1

do you know how to solve that?

 

[rbcc]

1/2+1/3+x=1

ok so first lets try to add 1/2 and 1/3, to do this we need a common denominator,

the easiest way to do this is by multiplying the denominator of each fraction by the other fraction, this is what I mean;

(1/2)(3/3) + (1/3)(2/2)
(3*1)/(2*3) +(2*1)/(3*2)
= 3/6+ 2/6

ok now that we have a common denominator, we can add the fractions, add the numerators and keep the same denominator
=5/6

now we have 5/6 +x =1 and we need to solve for x so we will isolate it.

we have to get rid of the 5/6 on the left side, since we have a +5/6 to get rid of that we need to subtract 5/6 from each side;

5/6+x-5/6=1-5/6

now we are left with x=1-5/6

ok so now we have a similar problem like in the first step, to subtract fractions we need a common denominator, 1 is like saying 1/1 so we have

1/1-5/6 try to solve that