Need help on the reasoning for the following ratios problem

[Optimist]

Hi

Stuck on the following, and just need help on a method more than an answer:

David's savings is four times that of Peter. When he spends £15 and Peter saves £45, both of them have the same amount of money. How much does each of them have in their savings at first?

[Guest55]

Well I said that if one spends £15 and the other saves £45 and they end up the same then this changes their difference by £60.

Difference = 3 lots of what Peter has (one has 4 times as much as the other)

so Peter must have £20.

Test:
David £80, Peter £20

then David £80 - £15 = £65
Peter £20 + £45 = £65

[Optimist]

Thanks Guest55

The answers showed:

3 units = £45 + £15 = £60

1 unit = £60 / 3 = £20

4 units = £20 X 4 = £80

David has £80 and Peter has £20 - both at first.

I prefer your (Guest55) explanation.

[Guest55]

Thanks! You are welcome ...

[Optimist]

Thanks! You are welcome ...

The worrying thing is that it is a Year 4 question!

[SleepyHead]

David's savings is four times that of Peter. When he spends £15 and Peter saves £45, both of them have the same amount of money. How much does each of them have in their savings at first?

Hi.. Would have done..

4a -15 =a + 45

So 3a =60

And a = 60/3

Very surprised it is a yr 4 question, please may I ask what source it's from?

Thanks
Sleepyhead

[Guest55]

No need to use algebra - you should really avoid it until it's abolutely necessary.

[KenR]

No need to use algebra - you should really avoid it until it's abolutely necessary.

Not sure I agree with that - the Durham CEM test often contains algebra questions in the Maths section so better that they get used to putting this practice

[Optimist]

Need help on the workings for the following question, please.

It takes 5 minutes to fry a beef burger. One side of the beef burger takes 3 minutes to fry and the other side takes only 2 minutes. Two beef burgers can be placed on the frying pan at a time. What is the shortest time to fry all five beef burgers?

The answer is not 15 mins, it is 13 minutes.

[Okanagan]

Code: Select all

minute | left side of pan | right side of pan
 1     |         A1       |        B1  
 2     |         A1       |        B1
 3     |         A1       |        B1  
 4     |         C1       |        B2
 5     |         C1       |        B2 
 6     |         C1       |        E1  
 7     |         C2       |        E1 
 8     |         C2       |        E1 
 9     |         D1       |        E2 
10     |         D1       |        E2 
11     |         D1       |        A2 
12     |         D2       |        A2 
13     |         D2       |          

or you could slot A2 (2nd side of burger A) in between B1 and B2 if you didn't want it to cool down too much between cooking each side!