Question 1122088: Anson had 5/7 the number of marbles Joel
Has. If Joel gives Anson 360 marbles, Anson will have twice as many marbles as Joel. How many marbles do they have together?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
x = amount of marbles Anson has currently
y = amount of marbles Joel has currently
x and y are positive whole numbers
The x and y values represent the respective marble counts before Joel hands over 360 marbles
The first equation is
x = (5/7)*y because "Anson had 5/7 the number of marbles Joel has"
"if Joel gives Anson 360 marbles, Anson will have twice as many marbles as Joel" tells us that x will bump up to x+360.
At the same time, y drops to y-360.
Tying the two ideas together gets us this second equation
x+360 = 2*(y-360)
Let's use substitution to find x and y
x+360 = 2*(y-360)
(5/7)*y+360 = 2*(y-360) ... replace x with (5/7)*y; see equation (1) above.
(5/7)*y+360 = 2*y-2*360
(5/7)*y+360 = 2*y-720
7 * [ (5/7)*y+360 ] = 7*(2*y-720)
5y+2520 = 14y-5040
2520+5040 = 14y-5y
7560 = 9y
9y = 7560
y = 7560/9
y = 840
Now that we know y, we can find x
x = (5/7)*y
x = (5/7)*840
x = 600
Before the transfer, Anson has 600 marbles and Joel has 840 marbles
After the transfer, Anson has 960 marbles and Joel has 480 marbles (600+360 = 960; 840-360=480)
No matter what point in time you're at (before or after the transfer), there is a total of 1440 marbles.
You can add 600 to 840 to get 1440, or you can add 960 to 480 to get the same answer.
Final Answer: 1440
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