Question 1172609
c = cesar's age.
m = melissa's age.
cesar is 52 years younger than melissa.
equation for that is c = m - 52
5 years ago, melissa was 3 times as old as cesar.
equation for that is m - 5 = 3 * (c - 5)
simplify that equation to get m - 5 = 3 * c - 15
you have two equations that need to be solved simultaneously.
they are:
c = m - 52
m - 5 = 3 * c - 15
rearrange the equations so that the variables are on the left and the constant terms are on the right.
you will get:
m - c = 52
m - 3c = -10
subtract the second equation from the first to get:
2c = 62
solve for c to get c = 31
in the equation of c = m - 52, replace c with 31 to get:
31 = m - 52
add 52 to both sides of this equation to get:
83 = m
you have:
c = 31
m = 83
your first original equation is satisfied because m - c = 52 becomes 83 - 31 = 52 which becomes 52 = 52 which is true.
your second original equation is satisfied because m - 5 = 3 * (c - 5) becomes 83 - 5 = 3 * (31 - 5) which becomes 78 = 3 * 26 which becomes 78 = 78 which is true.