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Adam and Friday's each had some money. If Adam spent $9, the ratio of the 

remaining amount of money Adam had to the amount of money that Firdaus 

had was 2:7. If Firdaus spent $9, the ratio of the amount of money Adam had

to the remaining amount of money that Firdaus had would become 7:11. How

much money did Adam and Firdaus have altogether at first?

 Feb 17, 2022
 #1
avatar+122390 
+1

Call the amount that Adam had originally  =  A

Call the amount that Friday  had originaly = F

 

We  have these two  equations

 

(A - 9) / F  =   2/7

A / ( F - 9)  =  7/11

 

Cross-multiply in each case

 

7 (A - 9)  = 2F

11A  = 7 (F - 9)                 simplify  both

 

7A  - 63   = 2F                      (1)

11A =  7F - 63                  rearrange  both as

 

7A - 2F  =  63

11A - 7F  = - 63            multiply  the first equation by -7   and the second by 2

 

-49A  + 14F  = -441

22A  -   14F  =  -126           add these

 

-27A  = -567

A = -567 / -27   =   21     ( Adam originally had $21  )

 

And using (1)  to find F

7(21)  - 63  =  2F

147 - 63  =  2F

84  = 2F

84/2   = F =   42    (   Friday originally had $42 )  

 

They originally had  $63  dollars combined

 

cool cool cool

 Feb 17, 2022
 #2
avatar+70 
0

It is supposed to be called Firdaus

tacoBRO1023  Feb 17, 2022
 #4
avatar+36417 
0

Yo, Taco....starts out as 'Friday'    then morphs to 'Firdaus' .....

ElectricPavlov  Feb 18, 2022
 #3
avatar+36417 
+1

(a-9) / f = 2/7          f = 7/2 (a-9)

 

a / (f-9) = 7/11        f = 11/7 a + 9      equate the two 'f's

 

7/2 ( a - 9 ) = 11/7 a + 9

1  13/14  a = 40.5

a = 21           then you can easily solve for f  = 7/2 ( a-9) = 42 dollars

 Feb 18, 2022
 #5
avatar+169 
+1

Adam = $x money

Firdaus = $y

(x - 9)/y = 2/7 -(1)

2y = 7(x - 9) = -(1)

    2y = 7x - 63 -(1)

 x/(y - 9) = 7/11

   11x = 7(y - 9)

   11x = 7y - 63 

2 (11x - 7y = -63)

7 (2y - 7x = -63)

  14y - 49x = -63 * 7

  22x - 14y = -63 * 2 

| - - - - - - - - - - - - - - - - - -
|       -27x = -567
|            x = 21
|            y = 42
|   x + y = $63
|
|
|

 Feb 20, 2022

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