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Three family members shared the cost of buying a flat equally. Adam used 1/2 of his savings, Bill used 6/7 of his savings and Carl used 3/4 of his savings. Bill and Carl had $44 820 left after paying for the flat.

(a) How much did the flat cost?

(b) How much does each of them have at first?

 Apr 2, 2022
 #1
avatar+122385 
+2

It's actually easier to answer (b) first

 

Let A  =  the amount that Adam started with

Let B  = the amount that Bill started with

Let C = the amount that Carl started with

 

We know that, since each paid an  equal amount, then

(1/2) A  = (6/7)B = (3/4) C

Which implies that

A =  (2/1)(6/7)B =  (12/7)B

C =  (4/3)(6/7)B = (24/21)B  =  (8/7)B

 

And we know that  

(1/7)B + (1/4)C   =  44820

 

So....subbing for C ,we have

 

(1/7)B   + (1/4)(8/7)B  =  44820

( 1/7)B + (8/28)B = 44820

( 1/7)B + ( 2/7)B =  44820

(3/7)B =  44820      mult both sides by 7/3

B = 44820 (7/3)   = $104580     what  Bill started with

A= (12/7)(104580) = $179280     what Adam started with

C = (8/7)(104580)  = $119520   what  Carl started with

 

And the flat cost

(6/7)(104580)  + (1/2)(179280)  +  (3/4)(119520)  =

 

$89640   + $89640   + $89640   = 

 

$268920

 

 

cool cool cool

 Apr 2, 2022
 #2
avatar+138 
+2

 

Let C - total rest of the flat

     x  - Adam's savings

     y - Bill's savings

     z - Carl's savings

Thus we know

C = 1/2x + 6/7y + 3/4z

Where 1/2x = 4/7y = 3/4z

Because the three of them shared the cost equally.

Now, y + z - 6/7y - 3/4z = 44,820

         1/7 + 1/4z = 44,820,

Since 6/7y = 3/4z,

         z = 4/7 (y)

         z = 8/7y

Hence,

       1/7y + 1/4 (y) = 44,820

       1/7 + 2/7y = 44,820

       3/7y = 44,820

            y = 7/3 (44,820)

            y = 104,580

Since z = 8/7y

          z = 8/7 (104,580)

          z = 119,520

Also,

Since 1/2x = 6/7y,

 

      x = 2(6/7)y

      x = 12/7y

      x = 12/7 (104,580)

      x = 179,280

Now, the total cost of the flat is

C = 1/2x + 6/7y + 3/4z

C = 1/2 (179,280) + 6/7 (104,580) + 3/4 (119,520)

C = 89,640 + 89,640 + 89,640

C = 268,920

 

Thus, the answers should be

(a) $268,920

(b) Adam's savings: $179,280

      Bill's saving: $104,580

      Carl's savings: $119,520

 Apr 2, 2022

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