Question 1172522
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.