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primary 6 | Maths
| Data Analysis
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Date Posted: 4 years ago
Views: 1033
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Trial and Error method:
At the start,
$2:$10
5 : 2
We try building a table of guesses to trial and error:
$2 | $10 | After exchange
5 , 2 》 15 , 0 (not possible to have ratio)
10 , 4 》 20 , 2 (the ratio is now 10:1)
15 , 6 》 25 , 4 (the ratio is now 25:4)
20 , 8 》 30 , 6 (the ratio is now 5:1) 《 correct
Tim had 8 $10 notes at first.
Algebra method:
Initial $2:$10 is 5x to 2x.
The exchange of notes and new ratio may be expressed as:
(5x+10)/(2x-2) = 5/1
10x-10 = 5x+10
5x = 20
x = 4
So Tim had 2(4) = 8 $10 notes at first.
At the start,
$2:$10
5 : 2
We try building a table of guesses to trial and error:
$2 | $10 | After exchange
5 , 2 》 15 , 0 (not possible to have ratio)
10 , 4 》 20 , 2 (the ratio is now 10:1)
15 , 6 》 25 , 4 (the ratio is now 25:4)
20 , 8 》 30 , 6 (the ratio is now 5:1) 《 correct
Tim had 8 $10 notes at first.
Algebra method:
Initial $2:$10 is 5x to 2x.
The exchange of notes and new ratio may be expressed as:
(5x+10)/(2x-2) = 5/1
10x-10 = 5x+10
5x = 20
x = 4
So Tim had 2(4) = 8 $10 notes at first.
Algebra method explained:
Since we do not know exactly how many $2 and $10 notes there are, we use an unknown called 'x' to create our equations.
Since the ratios of $2 to $10 notes is 5:2, we can say that:
Number of $2 notes = 5x (5 times unknown x)
Number of $10 notes = 2x (2 times unknown x)
Notice that whatever number x is, the ratio will always be 5 to 2.
When the exchange happens, the number of $2 notes increase by 10 and the number of $10 notes decrease by 2.
So we can write the new number of notes as:
New number of $2 notes = 5x + 10
New number of $10 notes = 2x - 2
And we know that the ratio of the new notes is 5:1, meaning that we can express their ratios as:
(5x + 10)/(2x - 2) = 5/1
Apply your cross multiplication, you get...
10x - 10 = 5x + 10
5x = 20
x = 4
We recall that the original number of $10 notes was represented by the term 2x, so that will be 8.
Hope this makes it clearer :)
Since we do not know exactly how many $2 and $10 notes there are, we use an unknown called 'x' to create our equations.
Since the ratios of $2 to $10 notes is 5:2, we can say that:
Number of $2 notes = 5x (5 times unknown x)
Number of $10 notes = 2x (2 times unknown x)
Notice that whatever number x is, the ratio will always be 5 to 2.
When the exchange happens, the number of $2 notes increase by 10 and the number of $10 notes decrease by 2.
So we can write the new number of notes as:
New number of $2 notes = 5x + 10
New number of $10 notes = 2x - 2
And we know that the ratio of the new notes is 5:1, meaning that we can express their ratios as:
(5x + 10)/(2x - 2) = 5/1
Apply your cross multiplication, you get...
10x - 10 = 5x + 10
5x = 20
x = 4
We recall that the original number of $10 notes was represented by the term 2x, so that will be 8.
Hope this makes it clearer :)
I understand up to the part before cross multiply, haha. Thanks for explaining.
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Explained this step on paper instead. Let me know if this helps! :)
Date Posted:
4 years ago
Btw, the arrows show you what multiplies with what.
Ok very clear now. :) Understand the working. Thank you very much!
Glad it helps :)
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I can explain the algebra one a little bit more if you are interested to understand (posting a separate answer).