Every year of a dog's life is worth 1 year of a human's life. If Rusty was a human, she would be twice the age of her owner, Mario. If Mario was a dog, he would be six years younger than Rusty. How old is Rusty?
Thank you for using the Jiskha Homework Help Forum. First of all, check the facts/typing in the first sentence. 1 year of a human life? Something wrong here.
To solve this problem, let's break it down into steps.
Step 1: Set up variables
Let's define two variables:
- Let R represent Rusty's age
- Let M represent Mario's age
Now we can translate the given information into equations.
Step 2: Translate the first piece of information
"Every year of a dog's life is worth 1 year of a human's life."
This means that if Rusty were a human, her age would be the same as her actual age. So we can write the equation: R = R.
Step 3: Translate the second piece of information
"If Rusty was a human, she would be twice the age of her owner, Mario."
If Rusty were a human, her age would be twice Mario's age. So we can write the equation: R = 2M.
Step 4: Translate the third piece of information
"If Mario was a dog, he would be six years younger than Rusty."
If Mario were a dog, his age would be six years less than Rusty's age. Since every year of a dog's life is worth one year of a human's life, we subtract six from Rusty's age. So we can write the equation: M = R - 6.
We now have a system of two equations with two variables (R and M).
Step 5: Solve the system of equations
We will use substitution to solve the system. Start with the second equation (R = 2M) and substitute it into the third equation (M = R - 6). Write the substitution as M = 2M - 6.
Now solve for M:
M - 2M = -6
-M = -6
M = 6
Step 6: Determine Rusty's age
Now that we know Mario's age (M = 6), we can substitute it back into the second equation (R = 2M) to find Rusty's age:
R = 2 * 6
R = 12
So Rusty is 12 years old.