Answer:
Eva's age = 24 years old
Eva's son's age = 6 years old
Explanation:
We can find the ages of Eva Santiago and her son using a system of equations where E represents Eva's age and S represents her son's age.
First equation:
Since Eva is currently 4 times as old as her son, our first equation is given by:
E = 4S
Second equation:
Since Eva was ten times as old as her son four years ago, our second equation is given by:
E - 4 = 10(S - 4)
Method to solve: Substitution:
Now we can substitute E = 4S for E in E - 4 = 10(S - 4) to find S, the son's age:
4S - 4 = 10(S - 4)
Distributing the 10 gives us:
(4S - 4 = 10S - 40) + 4
(4S = 10S - 36) - 10S
(-6S = -36) / -6
S = 6
Thus, the son is currently 6 years old.
Finding Eva's age:
Now, we can plug in 6 for S in E = 4S to find Eva's current age:
E = 4(6)
E = 24
Thus, Eva is currently 24 years old.
Checking the validity of our answers:
Since 24 is indeed 4 times 6, the first statement is satisfied.
Four years ago, Eva was 20 as 24 - 4 = 20 while her son was 2 as 6 - 4 = 2. Since 20 is indeed 10 times 2, the second statement is also satisfied.
Thus, our answers are correct.