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Bob has 3/4 as much money as Dan. Dan received another $15. As a result, Bob had 6/11 as much money as Dan. How much did Dan have at first?

 Jun 21, 2021
 #1
avatar+121000 
+2

B =  (3/4)D

 

After  Dan  received   $15   he  has    D  +  15

 

So

 

B  / ( D +  15)   =  6/11

 

(3/4)D  /  ( D + 15)  =  6 /11     cross-multiply

 

11 * ( 3/4)D  = 6 (D + 15)

 

(33/4)D    =  6D   +  90

 

(33/4)D  - 6D   =  90

 

(33/4)D   -  (24/4)D   =  90

 

(9/4)D  =  90

 

D  = (4/9) (90)  =     $40  = what Dan started with

 

 

cool cool cool

 Jun 21, 2021
 #2
avatar+33556 
+2

B = 3/4 D

 

Then    add 15 to D

B = 6/11(D+15)                Sub in the red equation

3/4D = 6/11D + 90/11

(33-24)/44 D = 90/11

D = 44/9 * 90/11 = 40 Dollars     (as CHris already showed !)

 Jun 21, 2021

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