Eric is twice as old as Ernest, who in turn is 5 years older than mike.if their total age is 47 years, how old is each of them?
M = Et - 5
Er = 2Et
Er + Et + M = 47
Substitute Et-5 for M and 2Et for Er in the third equation and solve for Et. Insert that value into the other equations to solve for M and Er. Check by putting all values into the third equation.
To solve this problem, let's break it down step by step:
1. Let's start by assigning variables to each person's age:
- Eric's age: E
- Ernest's age: N
- Mike's age: M
2. We know that Eric is twice as old as Ernest. So, we can write the equation: E = 2N.
3. We also know that Ernest is 5 years older than Mike. So, we can write the equation: N = M + 5.
4. Finally, we know that their total age is 47 years. So, we can write the equation: E + N + M = 47.
Now, let's substitute the values from equation 2 and equation 3 into equation 4 to get a simplified expression:
(2N) + N + (N - 5) = 47
Simplifying the equation, we get:
4N - 5 = 47
Adding 5 to both sides of the equation, we get:
4N = 52
Dividing both sides of the equation by 4, we get:
N = 13
Substituting this value back into equation 2, we can find Eric's age:
E = 2N = 2 * 13 = 26
Finally, substituting the value of N into equation 3, we can find Mike's age:
M = N - 5 = 13 - 5 = 8
So, the ages of each person are:
Eric is 26 years old.
Ernest is 13 years old.
Mike is 8 years old.