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?
+129852 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
+237
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
