Jill, Meg, and Beth are sisters. Jill is 2 years younger than Meg. Beth is half as old as Meg. Use the same variable to write three algebraic expressions based on this situation. Tell what the variable represents and what each expression represents.
x - 2= Meg
(1/2)x = Beth
Let x = Meg's age
According to the problem, Jill is 2 years younger than Meg:
Let x - 2 = Jill's age
And it was also said that Beth is half as old as Meg:
Let (1/2)x = Beth's age
Let's use the variable "m" to represent Meg's age.
1. Jill's age: m - 2
Here, the variable "m" represents Meg's age, and the expression "m - 2" represents Jill's age, as Jill is 2 years younger than Meg.
2. Beth's age: (1/2)m
Again, the variable "m" represents Meg's age, and the expression "(1/2)m" represents Beth's age, as Beth is half as old as Meg.
3. Meg's age: m
The variable "m" represents Meg's age, and the expression "m" simply represents Meg's age itself.
Let's use the variable "x" to represent Meg's age.
1) Meg - 2: This expression represents Jill's age. Since Jill is 2 years younger than Meg, we subtract 2 from Meg's age (x) to get Jill's age.
2) x / 2: This expression represents Beth's age. Since Beth is half as old as Meg, we divide Meg's age (x) by 2 to get Beth's age.
3) x: This expression represents Meg's age itself. It is simply equal to the variable x, which we defined as Meg's age.