Answer: To find out how old Eli is, we need to set up equations based on the given information.
Let's assume Ryan's age as "x".
According to the first statement, Eli is three times as old as Ryan, so Eli's age would be 3x.
According to the second statement, Eli is seven years older than Lucy. Let's assume Lucy's age as "y". Therefore, Eli's age would be y + 7.
The sum of their ages is given as 126, so we can set up the equation:
x + 3x + (y + 7) = 126
Simplifying the equation, we have:
4x + y + 7 = 126
Subtracting 7 from both sides of the equation, we get:
4x + y = 119
Now, we have one equation with two variables. To solve for Eli's age, we need another equation.
Since Eli is three times as old as Ryan, we can set up another equation:
3x = y + 7
We can solve this equation for y by isolating y:
y = 3x - 7
Now, we can substitute this expression for y in the first equation:
4x + (3x - 7) = 119
Simplifying the equation further:
7x - 7 = 119
Adding 7 to both sides of the equation:
7x = 126
Dividing both sides of the equation by 7, we find:
x = 18
Now, we can substitute this value of x back into the second equation to find y:
y = 3(18) - 7
y = 54 - 7
y = 47
So, Ryan is 18 years old and Lucy is 47 years old.
Finally, we can find Eli's age by substituting the values of x and y into the equation for Eli's age:
Eli's age = 3x = 3(18) = 54
Therefore, Eli is 54 years old.