To ask for maths help. Ratio!

[whoopstheregomyinsides]

My head is exploding because I don’t know the way to help my son do these and explain how it works. I’m normally ok at maths but this has me banging my head against the table. He hasn’t brought his class book to show me the method so I am struggling
Can anyone help please? Pics below of the questions

The baking one, we have to calculate ingredients for 20 biscuits - I just divide by 8 and multiply by 20 when I’m baking but suspect that won’t cut it here!

The biscuits one would be fine to divide by 8 and multiply by 20. Or to say that you need 20/8 of the original amount, which simplifies to 2.5

I can't read the one about the translation as a bit is cut off.

For the one about the savings, you could do algebra - depends a little on the age of the child. If he's younger, it might just be doing it trial and error, working out the ratio after each week.

if he is old enough to do algebra, you could do:

w = number of weeks.

18 + 4.5w = 4w x 15/8

(i.e., the four-pound a week saving is equal to 15/8 of the other person's savings).

Solve :

18 + 4.5 w = 60w/8
18 + 4.5w = 7.5w
18 = 3 w
w = 6

I would maybe attack if this way:

20 /8= 2.5.

So you’ll need 2.5x more ingredients to make 20x Biscuits than posted in original question to make 8x biscuits.

75g x 2.5 = 187.5g
50g x 2.5 = 125g
40g x 2.5 = 100g
2x egg x 2.5 =5 eggs

divide by 8 and multiply by 20 is right

other one don't know and I have had wine, sorry

The baking one you cannot divide egg by 8 so you can half it to make 4 biscuits then multiply it by 5 to make 20 biscuits

Of course you can divide 2 eggs by 8 - you aren't actually physically dividing them. 2/8 is 1/4 , or 0.25, which you can then multiply by any amount you want

But it makes more sense to think of it as 2.5, as that's easier to multiply by.

(or indeed, halving it and then multiplying by 5. All the same thing. But not because you can't divide by 8. Because it's easier numbers to do mentally this way)

ADAM

Add
Divide
and
multiply

So for the baking, there's nothing to add as each ingredient needs working out alone.

75g flour

Divide: 75/8 = 9.38
Multiply: 9.38 x 20 = 187.60g I would round up to 188g

2 eggs

Divide: 2/8 = 0.25
Mutiply: 0.25 x 20 = 5

The answer to the second one is 6 weeks.
After 6 weeks it would be £18+£27 (6×4.5) = £45 and 6×£4=£24, divide both by 3 to get a ratio of 15:8. DS says to just add up until it works, that's what he's always done

The baking I can do now by explaining we need to find a common multiple maybe? So divide by 2 to get 4 biscuits’ worth then multiply by 5
The translation one I’ll add a pic again

The savings one I need to re read the formula. We started writing it out week by week starting with 0 and 18 and adding it on but I don’t think that’s what teacher wants. She wants algebra I think. He’s year 8. Should have said that sorry. And thank you all. I’m off to open wine and start again with him

Sorry. Here’s the pic

another way to explain the algebra version would be to think of it like equivalent fractions:

(18 + 4.5w)/4w = 15/8

(would be easier if you could see horizontal lines for the fractions)

If you then multiply both sides by 4w, you can then continue it in the way I wrote above.

sorry, still not seeing enough of the photo to get the information needed for the translation one

The translation one, assuming I’ve read the missing info correctly:

Beth would take 8 days, M would take 10.

So B works at a rate of 1/8 per day, M at 1/10 per day.

Beth has already done 2 days work before M starts to help- so 2/8 or 1/4 of the documents were done. That leaves 3/4 of the documents to do.

We need to add B and M’s work rates to find out how fast they work together. You can’t add eighths and tenths unless you find a common denominator, easiest in this case is 80ths. So B works at 10/80 and M works at 8/80, together they work at 18/80 (which simplifies to 9/40)

We can now work out how quickly they can complete the remaining 3/4 of the documents. The first day they did 9/40. Second day they got to 18/40. 3rd day 27/40, meaning they only need a third of a day to get to 30/40 (which is the same as 3/4)

So the answer is 3 and a third days to finish.

The translation one- I'm assuming its 10 days for Mia, as that's in his answer.
I dont think he has taken into account 2 days of work has been done, so only 3/4 of a document left to do.

DD 12 says:
125g sugar
100g butter
187.5g flour
5 yolks

8:10 was the ratio he’d written sorry.
In the translation one, hasn’t 1/4 been don? Or 10/40? So 30/40 left to do ?

Yep, 3/4, or 30/40 left to do.