John's front lawn is 1/3 the size of his back lawn.

Fraction of unmoved lawn = Total un mowed lawn / Total Area
F - Front Lawn
B - Back Lawn

F = 1/3(B)

Total Area = F+B = 4F (or 4/3 B; lets keep it as 4F for simplicity)

Total un mowed = Remaining of Front + Remaining of Back;
"John mows 1/2 of his front lawn": so 1/2F remaining
"and mows 2/3 of his back lawn,": so 1/3 of B remaining; which is 1/3(3F) = F
Total un mowed = 3/2(F)

Fraction = \(\frac{3}{2}*F/4F\) = 3/8.

Ans: C

Hi
I tried this task too, but my result is wrong. I dont know why because our solution path seems similar.

5/6 of the back lawn is mowed. Means 1 /6B is not mowed.
The total lawn is 4 /3 lawn.

(1/6 B) / (4/3B) = 1/8 which is incorrect.

Why ?

Thanks in advance for your help.

Here we go:

Let the size of back lawn - 3
Then front lawn - 1
Total Lawn area = 4 ---- (1)

John mows 1/2 of his front lawn and 2/3 of his back lawn


Total lawn area left unmowed = 1/2 + 1 = 3/2 ---- (2)
Fraction = (2) / (1) = 3/8

Option C

According to me.....
5/6 of the total lawn is mowed as per your solution
and the total lawn is 4/3 (as per your solution)

So the lawn left unmowed will be given by (Total - Lawn mowed) ----> 4/3 - 5/6 = 1/2

and then (1/2) / (4/3) = 3/8

I hope that is clear now.

why couldn't it be in this way?

let back = B
front = 1/3B

done for front = 1/2*1/3B = 1/6B
done for back = 2/3B

combining workdone for front and back = 1/6 + 4/6 = 5/6B
what left to be done = (front + back) - (work done for front and back) = (1/3B + B) - 5/6B = 4/3B - 5/6B = 1/2B

ans. D?

pannathat , it looks as if it should work. I had to stare at it for a minute. But the question asks for the fraction left unmowed.

Thus your remaining amount, \(\frac{1}{2}B\), is the part. \(\frac{4}{3}B\) is the whole.

\(\frac{(\frac{1}{2})B}{(\frac{4}{3})B}\)= \(\frac{3}{8}\)

I think choosing numbers is easier on this question. Or, if algebra is preferred, maybe use whole numbers? Seems easier to see or remember the "fraction" part.

That is, maybe try front = F, back = 3F, whole = 4F

F(1/2 unmowed) = 1/2F left
3F(1/3 unmowed) = 1F left
Total left: \(\frac{3}{2}\)F
What remains as fraction of whole?
Whole = 4F

\(\frac{(\frac{3}{2})F}{4F}\)= \(\frac{3}{8}\)

Answer C

Hope it helps.

Let Back lawn = 6 ....then Front lawn = 2....total = 8 units

mowed = (1/2) (2) + ( 2/3) ( 6) = 1 + 4 = 5 units

unwoed = 8 - 5 =3 units

Fraction land unmowed = 3/8

Answer: C

Let the size of back lawn be 300. This means that front lawn is 100. He mowed 2/3rd of back lawn(=200) and moved 1/2 of front lawn (=50)

So, remaining to be mowed is 150/(300+100)

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