Jill is 2 years older than Mike. in 5 years, 5 times Mike's age will be 4 times Jill's age. how old is Mike? 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.

To solve the first question, let's represent Mike's current age as x. Since Jill is 2 years older than Mike, her age can be represented as x + 2.

In 5 years, Mike's age will be x + 5, and Jill's age will be (x + 2) + 5 = x + 7.

According to the problem, 5 times Mike's age in 5 years will be equal to 4 times Jill's age in 5 years. So, we can write the equation as:

5(x + 5) = 4(x + 7)

To solve this equation, distribute and simplify:

5x + 25 = 4x + 28

Subtract 4x from both sides:

x + 25 = 28

Subtract 25 from both sides:

x = 3

Therefore, Mike is currently 3 years old.

For the second question, let's assume that x represents your age. According to the question, the eldest person is a year older than you, so their age can be represented as x + 1.

To find the equation that models when the total ages add up to 150 years, we can add your age (x) to the eldest person's age (x + 1):

x + (x + 1) = 150

Simplifying:

2x + 1 = 150

Subtract 1 from both sides:

2x = 149

Divide both sides by 2:

x = 74.5

Therefore, your age is 74.5 years, and the eldest person's age is 74.5 + 1 = 75.5 years.