Question

Alice, Beryl and Charles donated some money to an orphanage. Alice contributed 2/5 of the donation. The remaining donation was contributed by Beryl and Charles in the ratio 3:7. Alice donated $792 more than Beryl. Find the amount of money Alice donated.

Answer 1

a = (2/5 ) d
b+c = (3/5) d
c = (7/3) b
b = a - 792
-----------------------
b + (7/3) b = (3/5) (5/2) a
(10/3)b = (15/10) a
(10/3)(a - 792) = 15 a / 10
a - 792 = 45 a /100
55 a /100 = 792
a = 1440

Answer 2

so, what do we know?
a/(b+c) = 2/3
b/c = 3/7
a = b+792
solve for a

Answer 3

Let the total donated be x
then A = 2x/5
B : C = 3:7 = 3y:7y ----> B+C = 10y

A = B+792
2x/5 = 3y + 792
2x = 15y + 3960 **

A+B+C = x
2x/5 + 10y = x
10y = 3x/5 ***

** times 2
4x = 30y + 7920
*** times 3 -----> 30y = 9x/5 , sub that into
4x = 30y + 7920
4x = 9x/5 + 7920
11x/5 = 7920
x = 3600

Alice donated (2/5)(3600) = 1440