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primary 6 | Maths
| Data Analysis
3 Answers Below
Anyone can contribute an answer, even non-tutors.
Pls help thanks
Date Posted: 3 years ago
Views: 833
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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.
Appreciate your help. I roughly understand the trial and error method but I am totally lost with the algebra one, haha. But thank you again!
It's okay, at this stage you're more or less expected to be familiar with the trial and error method instead.
I can explain the algebra one a little bit more if you are interested to understand (posting a separate answer).
I can explain the algebra one a little bit more if you are interested to understand (posting a separate answer).
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:
3 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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