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System of equations

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The difference between two numbers is 9. Three times the smaller is equal to twice the larger.  What are the numbers?

Sep 21, 2017

#1
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We make 2 equations(x is the smaller number; y is the bigger number):

y-x=9

3x=2y

y-x=9

y=(3x)/2

(3x)/2-x=9 => (3x)/2-(2x)/2=9 => x/2=9 => x=18

y=(3*18)/2 => y=54/2 => y=27

Therefore, x and y are 18 and 27 respectively.

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Sep 21, 2017
#3
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Thank you so much!

NediaMaster  Sep 21, 2017
#2
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The difference between two numbers is 9. Three times the smaller is equal to twice the larger.  What are the numbers?

Let the smaller number = S

Let the larger number =L

L - S = 9 ...........(1)

3S =2L..............(2)

From (1) we have:

L = 9 + S     sub into (2)

3S = 2(9 + S)

3S = 18 + 2S

3S - 2S = 18

S = 18 the smaller number.

L - 18 = 9

L = 9 + 18

L = 27 the larger number.

Sep 21, 2017
edited by Guest  Sep 21, 2017
#4
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Thank you so much!

NediaMaster  Sep 21, 2017
#5
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@Guest yeah that is a faster way I should've done that

Jeff123  Sep 21, 2017
#6
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too complicated!

Sep 21, 2017
#7
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I know! Thankfully the people above answered it for me

NediaMaster  Sep 21, 2017