3 variable ratios

Hi!
This kind of problem confuses me. For this particular one, I have the mark scheme but I don't understand why you have to do each step.

Could someone go through how you would do this question, why you do each step? + Help me outline a way of tackling them.

Thank you!

...

Out of interest, where did you get this question from?

Different methods. Here's one way:

From the question we know that 3 bricklayers can build 18 walls in 15 days. We can write this as a ratio to make things simpler:

3B : 18W : 15D

There are 5 days left and they need to build 19 walls (37 - 18). So we need to know how many bricklayers are needed to build 19 walls in 5 days. Looking back at the original ratio

3B : 18W : 15D

First lets change the number of days from 15 to 5. If the number of days decreases by a factor of 3 then it makes sense that we will require 3 times the amount of bricklayers to do this work since they have less time to do the work. So now we have

9B : 18W : 5D

So it will take 9 bricklayers 5 days to build 18 walls. We're nearly there but we need to know how many bricklayers are needed to build 19 walls in the same time period.

Can you carry on from here? Post your working/ideas if you get stuck.

Ooh...

9B : 18W : 5D
?B : 19W : 5D

19/18= 1.0555... 1.0555... * 9= 9.5
so ?= 9.5

9.5-3= 6.5 <- but you have to round up 7.

See, I understand it now but if that comes up in my exam, I'm not sure I will be able to see it immediately. :/

Which specific part are you not confident with?

Try writing problems like this as 3 variable ratios and manipulating them. With 3 variable ratios you can keep one variable constant and change the other two.

E.g. 3B : 18W : 15D

We could keep the number of walls constant and double the number of builders. This will mean we need fewer days:

6B : 18W : 7.5D

Or we could keep the number of builders constant and double the number of walls. This will mean we need more days:

3B : 36W : 30D

Try this with different questions. If you practice then you'll be fine