Set up an algebraic equation for this problem:When Brett and his younger sister add their ages together the sum in 17. Brett is not a teenager yet. In fact his age is not even a two-digit number. How old is Brett's sister?
B+Y=17
B<10
if B is 1, then S=17
if B is 9, then S=8
so, 8<S<17,
To set up an algebraic equation for this problem, we can use variables to represent Brett's age and his sister's age.
Let's say Brett's age is represented by the variable "B," and his sister's age is represented by the variable "S."
Given the information, we can write two equations:
1. The sum of their ages is 17: B + S = 17
2. Brett's age is not a two-digit number: B < 10
These two equations represent the problem described.
Now, we can solve for the age of Brett's sister by substituting the value of B from equation 2 into equation 1. By doing so, we will have a single equation with one variable:
B + S = 17
Since B < 10, we can substitute B = 1, 2, 3, 4, 5, 6, 7, 8, or 9 into the equation and check which value satisfies the equation.
For example, if we substitute B = 1, the equation becomes:
1 + S = 17
Simplifying the equation gives:
S = 17 - 1
S = 16
Therefore, if Brett's age is 1, his sister's age would be 16.
Repeat this process for each value of B, and you will find the correct age for Brett's sister, satisfying both equations.