SOLUTION: At first the number of Mac's marbles was 80% of Jack's marbles. After Mac had given 48 of his marbles to Jack, the number of his marbles left was half as many as Jack's marbles. Ho

Algebra ->  Percentages: Solvers, Trainers, Word Problems and pie charts -> SOLUTION: At first the number of Mac's marbles was 80% of Jack's marbles. After Mac had given 48 of his marbles to Jack, the number of his marbles left was half as many as Jack's marbles. Ho      Log On


   

Question 1172522: At first the number of Mac's marbles was 80% of Jack's marbles. After Mac had given 48 of his marbles to Jack, the number of his marbles left was half as many as Jack's marbles. How many marbles did Mac have at first?
Found 3 solutions by josgarithmetic, Theo, greenestamps:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
               MAC           JACK

ORIGINAL         m            j
ORIGINAL        0.8*j         j

STEP1           0.8j-48       j+48

RESULT         2(0.8j-48)=j+48

Not the only way, but 2%280.8j-48%29=j%2B48, solve, and then evaluate 0.8j.
--
1.6j-96=j%2B48
0.6j=48%2B96
j=%2848%2B96%29%2F%280.6%29
highlight_green%28j=240%29

4%2F5 of j is %284%2F5%29%2A240=highlight%28192=m%29.

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
x = number of marbles mac had
y = number of marbles jack had
number of mac's marbles were 80% of number of jack's marbles.
equation for that is x = .8 * y
after mac gives 48 of his marbles to jack, the number of marble he has left is half as many as number that jack has.
equation for that is x - 48 = .5 * (y + 48)
simplify to get x - 48 = .5 * y + 24
add 48 to both sides of that equation to get x = .5 * y + 72
you have:
x = .8 * y
x = .5 * y + 72
subtract second equation from the firt to get:
0 = .3 * y - 72
add 72 to both side of that equation to get:
72 = .3 * y
solve for y to get:
y = 72/.3 = 240.
x = .8 * y results in x = 192.
you have x = 192 and y = 240
your first equation of x = .8 * y becomes 192 = .8 * 240 which becomes 192 = 192 which is true.
your second equation of x - 48 = .5 * (y + 48) becomes 192 - 48 = .5 * (240 + 48) which b4ecomes 144 = .5 * 288 which becomes 144 = 144 which is true.
both original equations are true when x = 192 and y = 240, confirming the solution is correct.
the solution is that mac had 192 marbles to start.


Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


I personally would do a little work with the given information to set up the problem without the need to work with decimals.

Since 80% is 4/5, let the original numbers of marbles be 4x for Mac and 5x for Jack.

Then, after Mac gives 48 marbles to Jack, the numbers are 4x-48 and 5x+48.

At that point, the number of Mac's marbles is half the number of Jack's:

4x-48+=+%281%2F2%29%285x%2B48%29
8x-96+=+5x%2B48
3x+=+144
x+=+48

ANSWER: The number of marbles Jack started with was 4x = 4(48) = 192.