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
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) (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 , solve, and then evaluate .
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of j is . Answer by Theo(13342) (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.