Explanation to this maths question

[Blossom8]

Hi, I'm rubbish with problem solving. Any bright folk out there can explain how to get the answer to this maths question please? Thanks.

There are 100 snowdrops and crocuses in the garden.
There are 50 more snowdrops than crocuses.
How many crocuses are there?

Errr 50 surely?

Oh no misread sorry. 75 snowdrops, 25 crocuses.

50

25 crocuses, 75 snowdrops

s(snowdrop) + c(crocuses) = 100
s = c + 50
(c + 50) + c = 100
2c + 50 = 100
2c = 100 - 50 = 50
c = 50 / 2 = 25
so crocuses = 25, and snowdrops = 25 + 50 = 75

but depending on year group which doesn't use algebra yet, I think you have to do it trial and error way?

misread too. scrap that

Thanks Titchy. Answer is 25 but how did you arrive at that figure so I can explain to my DD in a simple way?

In algebra convert the two facts:

1. s + c = 100

1. s - c = 50

re-arrange so that c (which is what you're trying to find the value of) is on one side, so:

1. becomes c = 100 - s

1. becomes s = 50 + c which becomes c = s - 50

so s - 50 = 100 - s

re-arrange so s is on one side only, so 2s = 150, so s = 75, therefore c = 25.

How old is your little one? The algebra is only really introduced in year six to those who are capable.

If you little one is much younger than that they'd be expected to try out pairs of numbers that make 100. Trial and error. Number bonds are very important throughout primary education - I think most adults would work this out through use of their number bonds and simple subtraction rather than algebra.

Hope that helps.

Maybe this would help as a way of visualising the calculation without doing algebra.

There are 100 flowers altogether. We know if we put the crocuses and snowdrops in crocus-snowdrop pairs, there would be 50 extra snowdrops left over that can’t be paired up.

Let’s pick the 50 extra snowdrops first and take them indoors and put them in a vase.

Now we know there are 50 flowers left altogether in the garden (100 total – 50 snowdrops now indoors in a vase). Those 50 remaining are made up of equal numbers of snowdrops and crocuses that can be paired up. So there are 25 crocuses and 25 snowdrops in the garden.

Altogether there are therefore 25 crocuses (all in the garden) and 75 snowdrops (25 in the garden and 50 in the vase indoors).

What year group is she? I suspect this might be the sort of question that they start doing by trial and error and see if they can spot any patterns.

e.g.

If you starting by thinking there are 10 crocuses, then 60 snowdrops = 70 in total - so too few.

So let's try 20 crocuses, so 70 snowdrops = 90 in total, still not enough

30 crocuses, 80 snowdrops = 110 flowers so too many .... what number should we try next??

it is very straightforward, take away the 50 extra snowdrops from the hundred flowers, then divide the 50 remaining flowers equally between snow drops and crocuses.