Answer:
Carlos is 37 years old and Ella is 17.
Step-by-step explanation:
Let,
Carlos = c
Ella = e
If Carlos is 3 more than twice Ella's age, we get the equation:
2e + 3 = c (1)
Since the sum of their ages is 54, we get the equation:
c + e = 54 (2)
Now we have a system of equations.
Since equation number 1 already designated the value of c in terms of e, we can substitute it into the second equation.
(2e+3) + e = 54
Lets combine like terms and solve!
2e + e + 3 = 54
3e = 51
e = 17
Let's substitute e back into one of the equations to figure out the value of c. I'm going to use equation 1.
2e + 3 = c
2(17) + 3 = c
34 + 3 = c
37 = c
Let's substitute the values of c and e into the second equations to check our work! (We know c and e already fulfill the first equation as we substituted e into it to get c)
c + e = 54
37 + 17 = 54
54 = 54
Now that we've checked our work, we know our answer is correct! Carlos is 37 years old and Ella is 17.
