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.
a = (2/5 ) d
b+c = (3/5) d
c = (7/3) b
b = a - 792
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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
so, what do we know?
a/(b+c) = 2/3
b/c = 3/7
a = b+792
solve for a
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
To solve this problem, let's break it down step by step:
Step 1: Find the total donation amount
Let's assume the total donation amount is represented by x.
Step 2: Find Alice's contribution
Given that Alice contributed 2/5 of the donation, we can write the equation:
Alice's contribution = (2/5) * x
Step 3: Find the remaining donation amount
The remaining donation amount is the total donation amount minus Alice's contribution:
Remaining donation = x - (2/5) * x
Step 4: Express Beryl and Charles' contribution ratio
The ratio of Beryl and Charles' contributions is given as 3:7. To find the specific amounts, we need to express the ratio as a sum of the parts:
Beryl's contribution = (3/10) * (Remaining donation)
Charles's contribution = (7/10) * (Remaining donation)
Step 5: Express the given relationship between Alice and Beryl's contribution
Alice donated $792 more than Beryl, so we can write the equation:
Alice's contribution = Beryl's contribution + $792
Step 6: Solve the equation
Substitute the value of Alice's, Beryl's, and Charles' contributions from earlier equations into the relationship equation and solve for x.
(2/5) * x = (3/10) * (x - (2/5) * x) + $792 + (7/10) * (x - (2/5) * x)
Solving the equation, we find:
x = $3960
Step 7: Calculate Alice's contribution
Substitute the value of x into Alice's contribution equation:
Alice's contribution = (2/5) * $3960
Simplifying this expression, we find:
Alice's contribution = $1584
Therefore, Alice donated $1584.