Question 950655
let m = marcus age today.
let j = john age today.


john is 10 years older than marcus.


equation for this is j = m + 10


3 times johns age 5 years from now will be the same as 5 times marcus' age 5 years ago.


equation for this is 3 * (j + 5) = 5 * (m + 5)


you  have 2 equations that need to be solved simultaneously.


they are:


j = m + 10
3 * (j + 5) = 5 * (m + 5)


replace j in the second equation with (m + 10) that it is equal to from the first equation.


you get:


3 * ((m + 10) + 5) = 5 * (m + 5)


simplify to get:


3 * (m + 15) = 5 * (m + 5)


simplify further by performing the multiplication to get:


3 * m + 45 = 5 * m + 25


subtract 25 from both sides of the equation and subtract 3 * m from both sides of the equation to get:


45 - 25 = (5 * m) - (3 * m)


simplify to get:


20 = 2 * m


solve for m to get:


m = 10


if m = 10, then j = m + 10 becomes j = 20


you have:


m = 10
j = 20


how old is john now?


john is 20 years old today.
he is 10 years older than marcus who is 10 years old today.


5 years from  now john will be 25 and marcus will be 15.


3 times john's age 5 years from now is equal to 3 * 25 which is equal to 75.


5 time marcus' age 5 years from now is equal to 5 * 15 which is equal to 75.


original problems statements are true, so the solution must be good.