Let’s call the amount of money she started with “m”.
What this problem is saying is that “taking away 39 from m is equivalent to taking 3/4 of m.” What do “taking away 39 from,” “equivalent to,” and “3/4 of” translate to mathematically?
The equation is
Some observations:
- is defined only as long as , or
- wherever is defined, its value must be non-negative, so that is never positive
- by the definition of absolute value, we have if , and if . Then
If , the equation becomes
Taking the square of both sides gives
but since the discriminant is , there are no real solutions.
If , then
Taking squares gives
and solving by the quadratic formula gives two potential solutions,
which have approximate values of 8.49 and 26.51.
We know for any value of that . We have and , so only the first solution 8.49 is valid.
Answer:b) about 50,000 people
Step-by-step explanation: