School Students Algebra Quadratics
Difference of two squares Common Factors
Algebra Examples
Remember that mathematics questions are like sandwiches:
First Slice of bread Definitions i.e. Let x be ...
The Filling The calculations
Second Slice of bread Concluding sentence
When you use a letter then you must define that letter at the beginning of the question.
The answer should be able to be read without looking back at the question.
So make sure that your sandwich is a Healthy Gourmet one and not a Stale Basic one!
Example One
Ross has $61 and wants to divide the sum between Thomasine, Louis and Joshua. Thomasine has twice as much as Louis and Joshua has $5 less than Thomasine and Louis together. How much do all three have each?
Answer One
Start off by defining the variables, now you can do this part in several ways so do the one that suits you.
Let the amount Thomasine has be $ T
Let the amount Louis has be $ L
Let the amount Joshua has be $ J
From the question, we know that Thomasine has twice as much as Louis so,
T = 2L So now we can write 2L instead of T
From the question, we know that Joshua has $5 less than Thomasine and Louis together so,
J = (T + L ) - 5 if we replace T by 2L we get,
J = 2L + L- 5 = 3L - 5
So we now have all the amounts with just one letter which is what we want so that we can solve it.
We didn’t have to use the three letters as we did above but we could have gone straight to the one letter as follows,
Let the amount Louis has be $ L, so if Thomasine has twice as much as Louis then she has $ 2L. If Joshua has $5 less than Thomasine and Louis together then he has $ (2L + L- 5 ) or $ 3L - 5
Either of these ways are fine just make sure that the person reading the answer knows what the letter or letters stand for.
Back to the question, all three amounts add up to $61 as this is the amount Ross has to share.
2L + L + (3L - 5) = 61
Thomasine + Louis + Joshua = Total from Ross
So collecting all the letters and numbers together on different sides
6L = 61 + 5 = 66
We add all the letters together and add 5 to both sides so -5 + 5 = 0 on the left-hand side and we have +5 on the right-hand side.
You will probably think of that last step, as change the sign as you go over the equal sign. We should really remember why this works as well.
Back to the question,
6L = 66
Dividing both sides by 6, we find that L = 11
Now this is not the answer as you were asked for “ How much do all three have each? ”
2L + L + (3L - 5) = 61
Thomasine + Louis + Joshua = Total from Ross
$22 $11 $(33 - 5)
$28
That is the end of our calculations but not the end of the question!
We must end with a sentence.
Ross shares out $61 with Thomasine receiving $22, Louis receiving $11 and Joshua receiving $28.
