Maths brains! Help me please.

[HoobleDooble]

Helping my Yr6 DS with his homework and this one is twisting my mind. I'm thinking the 95 extra apples to pears is relevant but I'm well and truly stuck. Please help before my slightly hungover head explodes.

It's 60 pears and 180 apples.

Blimey that was fast! How did you work that out? I need to be able to explain it to a 10 year old.

The way you work it is:

1a = 3p
A - 150 = 2(p - 45)

Then you just substitute in:

3p - 150 =2p -90
P = 60

All the fruit is in rows of 4 to start with

Apple, Apple, Apple, Pear

After the 150 Apples and 45 Pears are removed whats left is in rows of 3

Apple, Apple, Pear

45 Pears are totally gone so all the apples they were next to to start with must be gone too.

So 45 x 3 apples are definitely gone (135)

But 150 Apples are gone so another 15 have been taken from the end of the last 15 rows leaving

Apple, apple, pear times 15

Is what I reckon.

3 times as many apples as pears to start with. If a is Original number of apples and p original number of pears then a=3p
3p (original number of apples)-150 = 2x (p- 45)
3p-150=2p-90
3p-2p= 150-90
P= 60
A=3x60=180

So at the start there were 45 rows that totally went and the 15 rows that are left

60 rows to start with, 60 pears, 60 x 3= 180 apples

Brilliant! In my muddled state I was doing 3a=1p ... no wonder I wasn't getting anywhere. Thank you so much.

You are not completely wrong, 3a for each 1p

I cheated and looked at someone else’s workings on this thread. I did mean to work it out for myself honest. I am ashamed of myself

So HeronLanyon could you make up a similar example with an answer of less than 100 fruits altogether to start witn?

tinsel I feel I am now in detention. Think it might be simpler to beg for an exclusion ?

Unless part eaten fruit could count - that would be about my limit right now.

@Notsurehowtofixit has shown how you can use algebra to solve a problem like this, but I am wondering if that is what is expected for a Y6? If you meet a problem like this that you don't have a learnt method to solve, then you maybe have to take a step back and try examples to see what might work.

So, I might say:

"3:1 - what would happen if I started with 300 apples and 100 pears? That would leave me with 150 apples and 55 pears, which is higher than 2:1.

"What about 240 apples and 80 pears? That would leave me with 90 apples and 35 pears, getting closer to 2:1"

"Obviously 150 apples and 50 pears is too low to start with, so the answer must be somewhere between 50 and 80 pears..."

daddaddad that’s exactly what I was starting to do when I became bored and cheated by looking at notsure’s answer paper above. To be fair notsure did nothing to protect their own work from my shameless behaviour and may even have encouraged it by displaying it so publicly !
I was then planning to extrapolate, from the answer, the method if possible.
I must say I thought this was extremely difficult for age of ds/dd !!

To elaborate on @Tinseloverthecracks solution - this picture might help.

Step (1): visualise the layout before and after (As and Ps inside the box are the ones removed).

Step (2): clearly this must be 45 rows given the pears are taken from here.

Step (3): multiply by 3 for 135 apples.

Step (4): 15 more apples needed to get the removal up to 150.

Step (5): so that's 15 more pears in those rows left in the box.

Step (6): 45 + 15 = 60.

I loved this tinseloverthecracks image further visualised by daddaddad.
Reminds me strongly of Cuisinaire Rods I used as a child to ‘see’ numbers/ratios etc. Beautiful things.