# Question

If Darren paid first, D : M : H = 4 : 9 : 11

If Hafiz paid first ,  D : M : H = 4 : 3 : 1 = 12 : 9 : 3

This is a good starting point as in both cases above, Muthu didn’t pay. Given Darren saved \$36 more than Muthu,

12u – 9u = 36

u =12

12u – 4u = 8u = 96

The cost of the gift was  \$96*3 = \$ 288

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```                        D :  M :  H
If Darren paid first:  4u : 9u : 11u
If Muthu paid first : 12u : 1u : 11u

(Note: Both sum up to 24u and Hafiz's money remained at 11u.
So this 2 ratios have compatible units and we need not scale.)

When either Darren or Muthu paid, they use 8u (12u-4u and 9u-1u).
So the portion of the gift they EACH paid is 8u.
This means originally they had 12u : 9u : 11u.

12u - 9u = 36 so u = 12.
EACH paid 8u = 8 x 12 = \$96.
Original gift cost 3 x 8u = 24u = 24 x 12 = \$288.

(PS: It seems the ratio 4:3:1 is not really needed to solve this.)
CHECK:
D     M     H
Start    144   108   132   = 12:9:11
D paid    48   108   132   =  4:9:11
M paid   144    12   132   = 12:1:11
H paid   144   108    36   = 12:9:3 = 4:3:1```

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