Sara is six years older than Ben. Five years ago, Sara was one and a half times ad old ad Ben. What is Sara's current age?
How did the teacher come up with Sara's current age of 23? I have no idea
s = b+6
s-5 = 3/2 (b-5)
so,
s-5 = 3/2(s-6-5)
s-5 = 3/2 (s-11)
2s-10 = 3s-33
s = 23
To find Sara's current age, we can create a system of equations based on the given information.
Let's assume Ben's current age is x.
According to the first statement, Sara is six years older than Ben. So, Sara's current age can be represented as x + 6.
Now, let's consider the second statement. Five years ago, Sara was one and a half times as old as Ben. We can represent this information as:
(Sara's age five years ago) = 1.5 * (Ben's age five years ago)
To simplify the equation, we need to subtract 5 from both the ages:
(Sara's current age - 5) = 1.5 * (Ben's current age - 5)
Substituting the values we got earlier, the equation becomes:
(x + 6 - 5) = 1.5 * (x - 5)
Simplifying further:
(x + 1) = 1.5(x - 5)
x + 1 = 1.5x - 7.5
0.5x = 8.5
x = 17
So, Ben's current age is 17.
Substituting this value in the equation we created earlier, we can find Sara's current age:
Sara's current age = x + 6 = 17 + 6 = 23
Therefore, Sara's current age is 23, based on the given information and solving the equations.