Of 6000 apples harvested, every third apple was too small, every fourth apple was too green, and every tenth apple was bruised. The remaining apples were perfect. How many apples were too small, too green, bruised, or perfect? What if n apples were harvested?
@ganeshie8

Question

Of 6000 apples harvested, every third apple was too small, every fourth apple was too green, and every tenth apple was bruised. The remaining apples were perfect. How many apples were too small, too green, bruised, or perfect? What if n apples were harvested?
@ganeshie8

ganeshie8 · Answer

`every third apple was too small,`

since you have `6000` apples, number of small apples would be   : 
$$\large \dfrac{6000}{3} $$

yes ?

anonymous · Answer

I think so

ganeshie8 · Answer

simplifying gives you  $\large  2000$

ganeshie8 · Answer

can you work # of green and bruised apples similarly?

anonymous · Answer

6000/4=1500
6000/10=600

ganeshie8 · Answer

yes!

ganeshie8 · Answer

what about perfect apples ?

ganeshie8 · Answer

and what about apples that are both too small and green   ?

anonymous · Answer

I did 6000/3 =2000 , 6000/4= 1500 then 2000+1500= 3500

ganeshie8 · Answer

so you're adding all the defective apples ?

ganeshie8 · Answer

looks you forgot the bruised ones

anonymous · Answer

when adding them all it would be 4100

ganeshie8 · Answer

yes don't you want to subtract the apples that are both too `small and green` ?

ganeshie8 · Answer

how many apples are both too `small and green` ?

ganeshie8 · Answer

` every third apple was too small, every fourth apple was too green and every tenth apple was bruised. `

that means every 12th apple is both too small and green
every 40th apple is both green and bruised
every 30th apple is both brused and too small

and every 60th apples all too small, green and bruised

ganeshie8 · Answer

Overall :
number of defective apples without repitition would be
$$\dfrac{6000}{3} + \dfrac{6000}{4} + \dfrac{6000}{10} - \dfrac{6000}{12} - \dfrac{6000}{40} - \dfrac{6000}{30} + \dfrac{6000}{60}$$

ganeshie8 · Answer

simplify and subtract that from 6000 for the number of good apples

anonymous · Answer

after doing the math that you put above I got 3150

ganeshie8 · Answer

yes! thats the count of  total defective apples

ganeshie8 · Answer

subtract it from 6000 for the good apples

anonymous · Answer

After subtracting 6000-3150 I got 2850

ganeshie8 · Answer

Looks good!

anonymous · Answer

I lady in my class said the answer is 2800 which the professor said could be right  but I don't see how

ganeshie8 · Answer

your lady is right, try again :
$$\dfrac{6000}{3} + \dfrac{6000}{4} + \dfrac{6000}{10} - \dfrac{6000}{12} - \dfrac{6000}{\color{Red}{20}} - \dfrac{6000}{30} + \dfrac{6000}{60}$$

anonymous · Answer

that doesn't add up either cause I got 3200

ganeshie8 · Answer

yes those are the defective apples

ganeshie8 · Answer

u still need to subtrct 3200 from 6000 for the good ones right?

anonymous · Answer

that works!

anonymous · Answer

how do I find out "What if n apples were harvested?"

anonymous · Answer

@mathstudent55

mathstudent55 · Answer

For n apples harvested, rewrite all the fractions you have with n in the numerator instead of 6000.

anonymous · Answer

so instead of saying 6000/ by all of the numbers it would be n*(1/3+1/4+1/10-1/12-1/20-1/30+1/60)

mathstudent55 · Answer

Yes.

anonymous · Answer

okay thanks i understand what i have to do now i just wasn't sure