Maths question Year 7 help please

[Creamegg11]

Can someone help how to work out the attached question please? I haven’t got the foggiest and husband doesn’t know either. Thanks

Write both known statements out with algebra:

X = 10c + 90w
X + 5 = 12c + 88w

Rearrange.

quite hard for year 7 I think!

If x is the number of L of water in the jug, then 10% of x is the amount of concentrate to start with, which you can write as 0.1x

If you then add 5 litres of concentrate, you now have 0.1x + 5 L of concentrate, and the new total volume is x + 5

At the same time, if the new amount of concentrate is 12% of the new solution, you can write that as 0.12 multiplied by the new total volume, and thus have an equation

So:

0.1x + 5 = 0.12 (x+5)

expand:

0.1x + 5 = 0.12x + 0.6

rearrange

4.4 = 0.02x

x = 220

So originally the jug has 220L of water, and 22L of concentrate (10%)

Add 5 litres of concentrate, and then you have 27 litres of concentrate, and a total volume of 225L, which is 12%

I would say y7 not the way titchy has done it as they will only just be learning algebra and won't be on to simultaneous equations. Plus it doesn't really meet part (a) of the question.

So I would use Thimbleberries method, but I might use fractions not decimals (many pupils won't immediately think of decimals for percentages), and then I would multiply both sides by 100 to get rid of the fractions.

x/100 + 5 = 12/100 * (x+5)

multiply both sides by 100

x + 500 = 12(x+5) now expand the brackets
x + 500 = 12x + 60 (now subtract 60 from both sides, and also subtract x from both sides)
440 = 11x now swap the two sides over so it looks better
11x = 440 now divide both sides by 11
x = 220

Mine isn't a simultaneous equation - there's only one unknown

I was suggesting a method of doing that would start the kid off rather than doing it for him!

Admittedly I misread the question though

I always try to assume on these threads that the parent isn't just going to show the whole thread to the child, but that the parent does need to see the whole solution to try to understand it.

It is difficult when we don't know whether the child is generally able at maths and just needs a push, or whether they are a struggler so need a fuller explanation.
Also whether it is question 1 or an extension task.

Has you child been learning about a specific type of equation in class. The homework is usually related to what they have been learning. So if they have been learning about simultaneous equations it may be related to that.

@TeenPlusTwenties

Your starting equation is incorrect, but somehow you ended at the right answer by making another error in your last step. (sorry if that's a bit blunt). So, I agree that x = 220, but 440 / 11 is not 220...

10x/100 + 5 = 12/100 * (x+5)

10x + 500 = 12 * (x+5)

10x + 500 = 12x + 60

440 = 2x

220 = x

That seems pretty challenging for even an able Y7 pupil.

Anyway, I wonder if the OP is coming back...

Oh how rubbish of me.
Shows how useless my brain is after all this pandemic lockdown and DD being out of education since April.

Don't beat yourself up - I was more intrigued how you ended up with the right answer anyway! I assume you did it on paper and it was just an error of transcription to the screen...

No worse than that.
I copied Thimbleberries' solution just looking at the screen and incorrectly transcribed to fractions. (I hate doing this kind of thing in decimals).

May I suggest a method which may be easier to explain to a year 7.
Start the equation by looking for something which is the same in both the start and end. The squash is changing, the concentrate is changing but the amount of water is staying the same. In the first it make s up 90% of the total liquid, which the question says to call x.
So the amount of water is 90x/100.
In the second it makes up 88%, ie 100-12. The amount of liquid has increased by 5 liters, so is x+5.
So the amount of water is 88(x+5)/100.
But the amount of water is the same so:
90x/100=88(x+5)/100
Multiply both sides by 100:
90x=88x+588
Take 88x from both sides
2x=588
Divide both sides by 2
x=5*44
x=220

Maths often has more than one way of finding solutions, so see which suits your dc best.

I also agree with other posters who have said to give your dc hints and see if they can work it out then. It will help them learn better.