Elliot is 5 times as old as Sid. Ten years from now, Elliot will be at least 3 times as old as Sid will be then. At least how old is each person now?
NOW:
Ted --- x
Ellito -- 5x
Ten Years From Now:
Ted --- x+10
Elliot -- 5x+10
"Elliot will be at least 3 times as old as Sid will be then"
5x+10 = 3(x+10)
solve
To solve this problem, let's assign variables to the ages of Elliot and Sid. Let's say Elliot's age is E, and Sid's age is S.
Given that "Elliot is 5 times as old as Sid," we can write the equation E = 5S.
We are also given that "Ten years from now, Elliot will be at least 3 times as old as Sid will be then." So, we can write the equation E + 10 ≥ 3(S + 10).
Now, let's solve the system of equations:
1. Substitute E from the first equation into the second equation:
5S + 10 ≥ 3(S + 10)
2. Distribute the 3 to both terms inside the parentheses:
5S + 10 ≥ 3S + 30
3. Combine like terms by subtracting 3S from both sides:
2S + 10 ≥ 30
4. Subtract 10 from both sides:
2S ≥ 20
5. Divide both sides by 2:
S ≥ 10
Therefore, Sid is at least 10 years old. Since Elliot is 5 times as old as Sid, Elliot is 5 times 10, which is 50 years old.
So, Sid is at least 10 years old, and Elliot is at least 50 years old.