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The difference between of two numbers, a and b, is 21. The difference of 5 times a and two times b is 18. What are the values of a and b?

 Apr 2, 2020
 #1
avatar+2152 
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Here are the equations:

 

a-b=21

5a-2b=18

 

Multiply the first equation by 5

 

5a-5b=105

5a-2b=18 --subtract--

 

-3b=87

b=-29

 

So, b=-29 and a=50

 Apr 2, 2020
 #2
avatar+112282 
+1

Using Cal's  equations  we  have  that

 

a  -  b   =  21    

5a  - 2b  =   18       

 

Multiply  the  first equation  through  by   -2

 

-2a  + 2b  = -42

5a  -  2b   =  18          add these

 

 

3a    =   - 24     divide  through  by  3

 

a =   -8

 

And

 

-8  - b  = 21

 

b  =  -8 - 21   =   -29

 

 

cool cool cool

 Apr 2, 2020

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