SOLUTION: Distribute $6,750 among Fred, Grace, and Aaron. Grace should receive twice as much as Fred and Aaron three times as much as Grace.

Question 168617: Distribute $6,750 among Fred, Grace, and Aaron. Grace should receive twice as much as Fred and Aaron three times as much as Grace.
Found 2 solutions by midwood_trail, josmiceli:
Answer by midwood_trail(310) (Show Source): You can put this solution on YOUR website!
Distribute $6,750 among Fred, Grace, and Aaron. Grace should receive twice as much as Fred and Aaron three times as much as Grace.
Fred = x
Grace = 2x
Aaron = 3(2x)
Then:
x + 2x + 3(2x) = 6750
x + 2x + 6x = 6750
9x = 6750
x = 6750/9
x = 750
Fred gets x or $750.
Grace gets 2x or 2(750) = $1,500
Aaron gets 3(2x) or 3(1500) = $4,500
I hope that helps.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
= amount Fred gets
= amount Grace gets
= amount Aaron gets
Given:
(1)
(2)
(3)
-------------
From (1)
(4)
Now substitute (2) and (4) into (3)
(3)
(4)
Multiply both sides by
(5)
(6)
(7)
Substitute this back in (2)
(2)
(8)
(9)
Substitute (7) into (4)
(4)
{10)
(11)
Fred gets $750, Grace gets $1500, Aaron gets $4500
check:
(1)
(2)
(3)
--------------
(1)
(12)
(13)
--------------
(2)
(14)
(15)
--------------
(3)
(16)
(17)
OK
RELATED QUESTIONS
Fred has 2 1/2 times as much money as his sister. Aaron has 3/4 as much money as Fred.... (answered by stanbon)
Fred is five times as old as grace. In eight years time, Fred will be three times as old... (answered by josgarithmetic,MathTherapy)
fred is five times as old as grace. in eight years time, fred will be three times ad old... (answered by josgarithmetic)
Distribute $3,750 among John, Maria, and Betsy so that Maria receives twice as much as... (answered by greenestamps,ikleyn)
Sally is twice as old as Fred four years ago Sally was three times as old as Fred how old (answered by josmiceli)
Julie is 4 times older than Aaron. In 10 years, Julie will be twice as old as Aaron.... (answered by checkley77)
Five years from ago, Zack was three times as old Aaron. Five years from now, Zack will be (answered by lwsshak3)
Grace and Janice had an equal amount of money at first. After Grace spent $245 and Janice (answered by josgarithmetic,ikleyn)
Divide $630 among Al, Bill and Carl so that Al will receive twice as much as Bill and... (answered by ankor@dixie-net.com)