Question 1118415
a equals the age of ali now.
m equals the age of mike now.


the ratio of ali's age to mike's age now is 5/3.


you get a/m = 5/3.


cross multiply to get 3a = 5m


solve for a to get a = 5m/3.


if ali was 7 years older and mike 7 years younger, then ali's age would be 3 times mike's age.


the equation for this is a + 7 = 3 * (m - 7


simplify to get a + 7 = 3m - 21.


solve for a to get a = 3m - 28.


you have two equations that need to be solved simultaneously.


they are:


a = 5m/3


a = 3m - 28


since 5m/3 and 3m - 28 are both equal to a, then they are equal to each other and you get:


5m/3 = 3m - 28.


muiltiply both sides of this equation by 3 to get:


5m = 9m - 84


subtract 9m from both sides of this equation to get -4m = -84.


divide both sides of this equation by -4 to get m = 21.


that's mike's age now.


the ali's age to mike's age now is 5/3 and from that we derived a = 5m/3.


a = 5m/3 becomes a = 5 * 21/3 which becomes a = 5 * 7 which becomes a = 35.


ali's age now is 35 and mike's age now is 21.


the ratio of ali's age now to mike's age now is 35/21 which is equal to 5/3.


if ali was 7 years older, he would be 42.


if mike was 7 years younger, he would be 14


3 * 14 = 42.


solution looks good.


solution is:


ali's age now is 35 and mike's age now is 21.