SOLUTION: Cesar is 52 yrs younger than Melissa. 5 yrs ago, Melissas age was 3 times Cesars age. How old is Cesar?

Question 1172609: Cesar is 52 yrs younger than Melissa. 5 yrs ago, Melissas age was 3 times Cesars age. How old is Cesar?
Found 3 solutions by ikleyn, greenestamps, Theo:
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.

Mental solution (reasoning)

5 years ago, Melissa was 52 years older than Cesar and thrice as old as Cesar. Hence, 5 years ago, Cesar was be 52/2 = 26 years old, while Melissa was 3*26 = 78 years old. It means that the Cesar's current age is 26+5 = 31 years. ANSWER

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Tutor @ikleyn is absolutely right to show a mental solution using logical reasoning. You get far more benefit from solving the problem by USING YOUR BRAIN than by performing some rote algebraic process.

However, if a formal algebraic solution is required....

We want to find Cesar's (current) age, so start by letting that be our variable, x.

Then Melissa's current age is 52 more than that: x+52.

So 5 years ago, Cesar's age was x-5, and Melissa's age was (x+52)-5 = x+47.

Write and solve the equation that says that 5 years ago Melissa's age was 3 times Cesar's age:

x+47 = 3(x-5)

Solve using basic algebra.

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
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.

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