Help with these fractions..=S (1 Viewer)

[ally66pr1nc3ss6]

I have just started a degree in primary teaching and we have to pass a maths test to get in and on the sample test papers this question had me stumped, it is probably very simple to do I just cannot remember how to do it.

So and so gave away 1/5, 1/3 and 1/6 of his apples, 18 apples remain. So how many apples were there initially?

Help on how to work that out would be much appreciated =]

[note: the use of calculators is not permitted.]

 

[cutemouse]

I have just started a degree in primary teaching and we have to pass a maths test to get in and on the sample test papers this question had me stumped, it is probably very simple to do I just cannot remember how to do it.

So and so gave away 1/5, 1/3 and 1/6 of his apples, 18 apples remain. So how many apples were there initially?

Help on how to work that out would be much appreciated =]

Umm... I assume he gave away 1/5 then gave away 1/3 of that and then 1/6 of that....

If so, he's given away (1/5)*(1/3)*(1/6) of his apples. So he's given away 1/90 of his apples, from the amount that he initially had.

If you let X be the amount of apple the person initially had then X*(1/90)=18, X=1620... The person initially had 1620 apples.

I don't know if this is correct, so feel free to comment if I'm wrong

 

[Continuum]

Nah, it's right jm

 

[Kujah]

Are the respective 1/5, 1/6 and 1/3 out of the original number of apples or as she gives them away individually?

 

[lolokay]

kujah is correct (his post under this)

and as his method shows, it's usually best to set these up as algebra problems, letting the unknown quantity be x (for example)

 

[Kujah]

So this is right:

^There are too many apples Correct me if I'm wrong with this, I haven't done maths for ages!

Okay, let x = total number of apples.

x/5 + x/3 + x/6 = x - 18

Basically, the addition of 1/5, 1/3 and 1/6 of the total number of apples will equal the apples that have been given away.

So,

6x + 10x + 5x / 30 = x - 18 (through LCD and all that)

21x/ 30 = x -18

21x = 30x - 540

9x = 540

x = 60

Test it out to see if it works:
1/5 of 60 = 12
1/3 of 60 = 20
1/6 of 60 = 10

Answer = 42 apples have been given away from a total of 60 apples, meaning that 18 are left.

 

[untouchablecuz]

Umm... I assume he gave away 1/5 then gave away 1/3 of that and then 1/6 of that....

If so, he's given away (1/5)*(1/3)*(1/6) of his apples. So he's given away 1/90 of his apples, from the amount that he initially had.

If you let X be the amount of apple the person initially had then X*(1/90)=18, X=1620... The person initially had 1620 apples.

I don't know if this is correct, so feel free to comment if I'm wrong

i THINK your wrong, correct me if i'm wrong

let the original amount of apples = x

so from the original amount of apples, 1/5, 1/3 and 1/6 apples were removed with 18 remaining

that is,

(the original amount) - (x/5 + x/3+x/6) = 18

x - (x/5 + x/3 + x/6) = 18

Solving for x we get 60 apples initially

 

[ally66pr1nc3ss6]

Are the respective 1/5, 1/6 and 1/3 out of the original number of apples or as she gives them away individually?

I am assuming that they are given away from the original number of apples as the question states:
"Eric had a box of apples. He gave 1/5 to so and so, 1/3 to someone else and a 1/6 to another person. There were still 18 apples remaining in the box. How many apples were there originally?"


Thanks for everyone's help. I'll have to write it down and see if I can work it out. Although I'm not sure who was correct =s

 

[ally66pr1nc3ss6]

So this is right:

^There are too many apples Correct me if I'm wrong with this, I haven't done maths for ages!

Okay, let x = total number of apples.

x/5 + x/3 + x/6 = x - 18

Basically, the addition of 1/5, 1/3 and 1/6 of the total number of apples will equal the apples that have been given away.

So,

6x + 10x + 5x / 30 = x - 18 (through LCD and all that)

21x/ 30 = x -18

21x = 30x - 540

9x = 540

x = 60

Test it out to see if it works:
1/5 of 60 = 12
1/3 of 60 = 20
1/6 of 60 = 10

Answer = 42 apples have been given away from a total of 60 apples, meaning that 18 are left.

Thanks heaps. But I'm not sure whether I understand the working out towards the answer. The answer seems right I just don't get how you got there.

In particular "6x + 10x + 5x / 30 = x - 18 (through LCD and all that)"
=S may have to elaborate a bit as I haven't done maths in a long time either.. sorry =[

 

[Kujah]

Okay, so we had x/5 + x/3 + x/6 = x-18.

For the left hand side, we want to find a common number for the denominators. 30 comes to mind, and is the closest option. We multiply the numerator and denominator by 6 to get 6x/30, x/3 by 10 to get 10x/30 and x/6 by 5 to get 5x/30.

Since we have 6x/30 + 10x/30 + 5x/30, its just simply a method of then adding the numerators together to get 21x/30.

After that, we cross-multiply.

 

[ally66pr1nc3ss6]

Okay, so we had x/5 + x/3 + x/6 = x-18.

For the left hand side, we want to find a common number for the denominators. 30 comes to mind, and is the closest option. We multiply the numerator and denominator by 6 to get 6x/30, x/3 by 10 to get 10x/30 and x/6 by 5 to get 5x/30.

Since we have 6x/30 + 10x/30 + 5x/30, its just simply a method of then adding the numerators together to get 21x/30.

After that, we cross-multiply.

I get you =]
Thanks heaps.

 

[PC]

But if this is for PRIMARY school, will they be using algebra at all? Can we do it without algebra?

If so and so gave away 1/5, 1/3 and 1/6 of the original amount, then ...

1/5 + 1/3 + 1/6 = 6/30 + 10/30 + 5/30 = 21/30 have been given away.
That means that 9/30 of the original amount remain.
So 9/30 of original amount = 18 apples.
Divide by 9.
1/30 of original amount = 2 apples
Multiply by 30.
Original amount = 60 apples

If the fractions apply to the number of apples present at each stage, then it's much harder, but just work backwards.

1/6 of the total were given away, so 5/6 remain, and this is 18 apples.
Divide by 5.
1/6 of total = 18/5
Multiply by 6.
Total = 21 3/5

1/3 of total were given away, so 2/3 remain, and this is 21 3/5 apples.
Divide by 2.
1/3 of total = 10 4/5
Multiply by 3.
Total = 32 2/5

1/5 of total were given away, so 4/5 remain, and this is 32 2/5 apples.
Divide by 4.
1/5 of total = 8 1/10
Multiply by 5.
Total = 40 1/2

So we started with 40 1/2 apples.

That doesn't make sense, so I reckon it's the first way.

 

[lolokay]

well you don't add/multiply fractions either in primary school

the question is just to test your mathematical ability. it doesn't necessarily need to be a primary school problem.

 

[dux&src]

^ the first way is right
Nice work guys.

 

[PC]

well you don't add/multiply fractions either in primary school

Serious? What primary school did you go to? I was doing that in Year 5!

 

[LobbSACS]

well you don't add/multiply fractions either in primary school

the question is just to test your mathematical ability. it doesn't necessarily need to be a primary school problem.

i did, in from year 5 onwards rofl.

 

[lolokay]

wtf we didnt learn that until high school

 

[LobbSACS]

well, we were taught it in year 5 and 6, i didnt pay any attention to it untill about year 11