Question

Lee is going to the US. He has 5 months & has worked out the following itinerary. He will be in A for 1 & a half months, in B for 1 & 2 thirds of a month & in C for 3 quarters of a month. The other place is D. How much time will he spend in D?

Answer 1

`1+1/12`
One month and eleven twelvs.

Explanation:

("A" means the time spend at A and so on)
`5=A+B+C+D`
`5=1+1/2+1+2/3+3/4+D`
`5=2+1/2+2/3+3/4+D`
`1/2+3/4=2/4+3/4=5/4=1+1/4`
`5=3+1/4+2/3+D`
`1/4+2/3=3/12+8/12=11/12`
`5=3+11/12+D|-3-11/12`
`1+1/12=D`

Answer 2

`1 1/2` months

Explanation:

The time in the U.S. would be equal to the time he spent in each of the places or:

`"time in US" = A + B + C + D`

We know some of these values, so lets plug them in:

`5= (1 1/2) + (1 2/3) + (3/4) + D`

Remove the parentheses and add like terms and subtract:

`5= color(blue)1 + 1/2 + color(blue)1 + 2/3 + 3/4 + D`

`5= color(blue)2 + 1/2 + 2/3 + 3/4 + D`

`color(red)3= 1/2 + 2/3 + 3/4 + D`

Now we will add the three fractions together. First, they all need to have the same denominator, so let's change that:
`1/2 rarr 6/color(orange)12`

`2/3 rarr 8/color(orange)12`

`3/4 rarr 9/color(orange)12`

Now put these new values back into the equation and add the numerators:

`3= 6/12 + 8/12 + 9/12 + D`

`3= 23/12 + D`

Simplify by changing into a mixed number `23/12 rarr 1 1/12`

Subtract `1`, and then subtract `1/2`
`3= 1 + 1/2 + D`
`2 = 1/2 + D`
`1 1/2 = D`