It costs $15 to attend a golf club with a local pro. Buckets of balls for practice during the club cost $5 each. Select the corr
1 answer:
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First you need to find the area of the whole circle.
The radius is given as 10, so just insert 10 into the equation of the area of a circle equation.
Putting
after the 100 because that is what is commonly done.
Because the circle is then being split into 4 equal sections, we need to find 1/4 of the area of the whole circle to find the area of one of these sections.
Since the area of the whole circle is
then we just divide that by 4,
leaving us with 25 and that is our final answer
The radius is given as 10, so just insert 10 into the equation of the area of a circle equation.
Putting
Because the circle is then being split into 4 equal sections, we need to find 1/4 of the area of the whole circle to find the area of one of these sections.
Since the area of the whole circle is
leaving us with 25
Let's call the two numbers and
.
Given these variables, we can say: , based on the first sentence in the problem.
Also, remember that the reciprocal of a number is simply 1 divided by the number. Thus, we can say that:
To solve, we can simply substitute in for
in the second equation and solve.
- Set up
- Get terms on the left side to a common denominator for easier addition
- Simplify
- Cross multiplication (
)
- Simplify
- Subtract
from both sides of the equation
- Factor left side of the equation
- Zero Product Property
Now, notice that we have found two solutions, but the problem is only asking for one. This <em>likely </em>means that one of our solutions is extraneous. Let's take a look. Remember that the smaller positive number is equal to 14 less than the larger number. However,
,
Since is not positive in this case,
is not a solution.
Thus, is our only solution. In this case,
,
which means that the smaller number is 14 and the larger number is 28.