He donated money to 3 organizations. He gave 8/15 to Red Crescent Society, 3/5 of the balance to the orphanage and remaining $7000 to a school.

Question

Find how much he donated to the orphanage?

I highly appreciate if someone is willing to teach me.

Answer 1

X is the total amount

 

Since he gave 8/15 to the Red Crescent Society,

there is 1 - 8/15 = 7/15 remaining. Of that, he

donated 3/5 of the the remaining balance to the orphanage.

 

X = 8/15X + 3/5(7/15)X + 7000

 

X = 8/15X + 21/75X + 7000 <--- multiplies the fractions

 

X = 40/75X + 21/75X + 7000 <--- common denominator

 

X = 61/75X + 7000 <--- adds the fractions with common denominator and combines like terms

 

1X = 61/75X + 7000

 

1X - 61/75X = 7000 <--- subtracts 61/75 X from both sides

 

75/75X - 61/75X = 7000 <---- subtracts the fractions with common denominator and combines like terms again

 

14/75X = 7000 <---- solves for X

 

X = 7000 * 75/14  <---- multiplies both sides by the reciprocal

 

X = 37500

 

Check:

 

Starts with $37500

 

8/15 or 37500 = 20000 <--- donated to Red Crescent Society

37500 - 20000 = 17500 <------ remaining balance

 

3/5 of 17500 = 10500 <---- donated to orphanage

 

17500 - 10500 = 7000 <---- remaining $7000 given to the school

 

$37,500 was donated to the three organisations, proven, verified, and checked