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# It’s hard

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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
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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   Apr 2, 2022
#2
+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