Using the information from the final statement in green, ‘162 green sweets, how many sweets did Mo start with?’
We know from the above that the final (target) amount of green sweets is 162, let’s give this a name… TotalGreenSweets
Moving upwards to the next statement, ‘Mo buys himself 30 more green sweets’
We worked out from the step previously that the TotalGreenSweets = 162 at the END, this is where problem solving questions tend to trip people up as we aren’t used to getting an answer and working backwards…
We can number each bullet point in the question to ensure we don’t get lost, e.g. GreenSweetsBP3 means the green sweets at bullet point 3…(see picture to left)
So if Mo buys 30 more sweets, that would mean has to equal our final statement:
As a formula, gives:
Putting in some values from the question, we know TotalGreenSweets = 162 and GreenSweetsBP3 is the value we are more interested in.
Therefore, if the total is 162 and we bought 30 NEW GREEN SWEETS, GreenSweetsBP3 must be the total BEFORE we bought 30 more. So the equation becomes,
Moving to our next bullet point, to be consistent we will call the green sweets at this stage GreenSweetsBP2,
The statement says, ‘3/4 of the sweets left over are green’, this means that the amount of green sweets we found previously, GreenSweetsBP3, is 3/4s the amount of green.
If we know that 3/4s = 0.75 (75%), we need to think of a number that will give us 100% (1/1)….
As an equation…
One of the ‘nice things’ about fractions is that if we want to know 100% of a known number, we just need to turn it upside down and multiply by the amount of green sweets at that stage…
This means our will be
The first bullet point is similar to what we just done in the last step (flipping fractions)
If we call the sweets at this stage GreenSweetsBP1 or SweetsInitial as we have a mixture of red and green now.
It says, ‘He eats 1/3 of the sweets’… if there are 176 sweets after he has eaten 1/3rd this means the sweets he has at is 2/3rd the initial value (SweetsInitial)…
(This is where it would be very easy to slip up, at the end where its most dangerous)
Similar to before, if we know that
We can flip to
to get our NewFraction.
All that is left is to multiply by the new fraction (because we only had a ratio of green sweets)…