12÷15<u /><em />=160
you have to divide 12 by 15 percent to get the missing number
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.


- Get terms on the left side to a common denominator for easier addition


- Cross multiplication (
)


- Subtract
from both sides of the equation

- Factor left side of the equation

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.
So we need to find the sum of the first 5 terms.
You have told me that the first term is 10 meters, and that r = 0.5 per term.
With this knowledge, we can use the formula s_n=a₁((1-r^n)/(1-r)).
Plugging in the terms that we know...
s₅=10((1-0.5⁵)/(1-0.5))
s₅=10(0.96875/0.5)
s₅=10(1.9375)
s₅=19.375
With s₅, we can determine that the ball has traveled a total of 19.375 meters after 5 bounces.