use the names and ages of yourself and the other two people you selected. Make sure one is older than you and one is younger than you.
In years, how old was the older person when you were born?
Write an equation that models how old in years each of you will be, when your ages add up to 150 years old. For example, if x = your age and the eldest person was a year older than you, you would write their age as x + 1. Then the equation would be: x + (x+1) = 150.
Explain the reasoning which helped you develop your equation.
Solve for your future ages. Are your answers reasonable, do they add up to 150?
In years, how old were you when the youngest person was born?
At some point during the lives of you and the youngest person, your age will be three times his/her age at that moment. Write an equation which models how old in years each of you will be when you are three times as old as the younger person.
Explain the reasoning which helped you develop your equation.
Solve the equation for your ages when you are three times as old as the youngest person. Are your answers reasonable?
To answer these questions, we need to know the names and ages of yourself and the other two people you selected. Let's assume your name is Alice, the older person's name is Bob, and the younger person's name is Charlie.
Let's say your age is x, Bob's age is y, and Charlie's age is z.
1. In order to find out how old the older person (Bob) was when you were born, we subtract your age from his age:
Bob's age when Alice was born = y - x
2. To create an equation that models how old each of you will be when your ages add up to 150, we add all three ages together:
x + y + z = 150
The reasoning behind this equation is that the sum of your ages (x + y + z) will eventually add up to 150, as time progresses.
3. To solve for your future ages, you would need additional information about the specific ages of you, Bob, and Charlie. Once you know the ages, you can substitute them into the equation (x + y + z = 150) and see if the sum is indeed 150. If it is, then the answers are reasonable.
4. To find out how old you were when the youngest person (Charlie) was born, we subtract their age from yours:
Alice's age when Charlie was born = x - z
5. To create an equation that models when you are three times as old as the youngest person (Charlie), we can set up an equation:
x = 3z
The reasoning behind this equation is that at some point during your lives, your age (x) will be three times the age of the youngest person (z).
6. To solve the equation for your ages when you are three times as old as the youngest person, you would need the specific ages of you and Charlie. Substitute Charlie's age into the equation (x = 3z), and check if the equation is correct. If it is, then the answers are reasonable.