Can someone help me with this maths question?

[MrsFogi]

I'm stumped on how a yr 4/5 would do this (I suspect using ratios but I must admit to being stuck). Can someone work through the workings to get an answer to this (so that I can then explain it to dd and look like I worked it out myself thereby demonstrating a love of maths and much grit and determination ):
A bag of compost and a bag of sand together weigh 25kg
A bag of compost and a bag of grit together weigh 22.5kg
A bag of sand and a bag of grit together weigh 17.5kg
Find the mass in kg of:
a) a bag of compost
b) a bag of sand
c) a bag of grit

Ok add the first two together the you get

2 compost + sand + grit = 47.5

Take off sand + grit which you know is 17.5

Leaves 2 compost = 30

From there you can get sand and grit...

Compost = 15kg
Sand = 10kg
Grit = 7.5kg

I can't tell you how I worked it out though as its all a jumbled mess in my head. Was never good at writing it down when worked out in my head. I started off with working out the difference between the first two was 2.5kg and went from there.

The sand must weigh 2.5kgs more than the grit. Based on the first two equations.
So take 2.5 away from 17.5 and divide that by two to get the weight of the grit. (7.5kgs)
Add the 2.5 to get the weight of the sand (10kgs)
And then 22.5kgs minus the grit is 15kgs for the compost.
As a check compost (15kgs),plus grit (7.5kgs) equals 22.5kg as given in the third equation.

Basically very long winded algebra.

Sand is 10kg
Grit is 7.5 kg
Compost is 15kg

Will show the working out in a mo

I would do it exactly the way Petra has done. 2 compost = 30, 1 compost = 15. Then you can work out by subtraction the weight of the sand and grit as Lemony pea has done.

(i) C + S = 25
(ii) C + G = 22.5
(iii) S + G = 17.5

Subract (ii) from (i) to get S - G = 2.5. If you add this result to (iii) the G will disappear and you'll get 2S = 20. So S = 10. Put this value of S into (i) which gives C = 15. Put this value of C into (ii) which gives G = 7.5. Check that these values work in the originally presented example to confirm.

What everyone else said. It's simultaneous equations.

Can we do another one now?

Got distracted by the fact that they are mixing weight and mass which are two different things....

Thank you all! Clearly I need some remedial classes in simultaneous equations!

I would encourage your dd to work it out with hints from you. Start by saying you are going to call the weight of the compost "c", etc. to reinforce the algebra notation. Then look at the first two equations. Which is heavier, the sand or the grit, s or g? Can she then say how much heavier? If she struggles, draw bags marked c and s sitting on some scales. Then c and g. Children often find visual clues make maths easier.

Once she has got to the sand being 2.5 kg heavier than the grit explain that it means you would have to add 2.5kg to the grit to make them the same weight so again reinforce the algebra by writing s=g+2.5.

Then get her to look at the last equation. You have s+g=17.5. But she knows that s=g+2.5. So if she were to put a bag of grit on the scales instead of sand she would also have to put on 2.5 kg as well to get the same weight. So instead of s she can write g+2.5 in the third equation.
So g+2.5+g=17.5.
Again draw it out if this helps her.
From this she gets to 2g+2.5=17.5 by collecting like terms.
Taking 2.5 from both sides you get to 2g=15.

It is important to get her to work it out rather than just showing her.

The aim of presenting children with maths problems is getting them to think mathematically. It's for them - on their own, in pairs or more - to visualise the problem and to arrive at a strategy for solving it using only the mathematical knowledge & skills they already possess. If an adult works it out their way, no doubt using algebra then attempts to explain their method to the children then they have been denied the opportunity to think for themselves. I would expect imaginative & confident KS2 kids to maybe sketch the bags or even quickly make & label them. But if they can't get started then
absolute minimal scaffolding from an adult.

I'm guessing at that age from a curriculum point of view they are supposed to be working it out by a trial and error type simple sum way rather than as simultaneous equations. Even though personally I'd look at and solve it as simple simultaneous equations.

I'm sure rouxle is right, and I'm assuming Y4s don't know how to do simultaneous equations. If DD was nowhere near, there's no point completely doing it for her.

However if I needed to explain it, looking at equ 2 and 3, compost weighs 5kg more than sand. Imagine swapping the compost for a bag of sand and a 5kg weight. So looking at Equ 1, you could say 2 bags of sand plus a 5kg weight is 25kg, so a bag of sand is 10kg.

Then add 5kg to get the weight of the compost, and equ 3 gives you grit.

Or you could say each one is roughly 10kg, with grit being lighter, and try different values.

Alternatively suggest a four year old should be playing with sand and making a mess, not doing this kind of homework. Ridiculous.

toohard it's y4/5. So age 9 or 10.

Ahhhh sorry missed that. Sorry for interrupting the maths lesson ;)