<span>x−27=67 solve for x
Add 27 to both sides, then
x -27 +27 = 67 + 27
x = 94
</span>
Let current age be x, next we construct the inequalities for the age:
<span>Four-fifths of my current age is greater than three-quarters of my age one year from now.
</span>thus when we add 1 year to 3/4 of our current age and set the inequality
4x/5>3x/4+1......i
<span>Four-fifths of my current age is also greater than five-sixths of my age one year ago.
Thus when we subtract 1 from 5x/6 and set the inequality we get
4x/5>5x/6-1.......ii
solving the inequalities we obtain:
</span>4x/5>3x/4+1
x/20>1
hence multiplying both sides by 20 we obtain:
x>20
also
4x/5>5x/6-1
4x/5-5x/5>-1
-x/30>-1
multiplying both sides by 30 we get:
-x>-30
thus
x<30
therefore the possible values of my age will lie in the interval:
20<x<30
Thus our age is in the interval
(20,30)
Answer:
Yolanda will have a balance of $34,043.10 in 14 years.
Step-by-step explanation:
This is an Ordinary annuity question where you pick the hint from the equal and recurring monthly payment.
To find the Future value of Yolanda's savings after 14 years, use Future value of annuity formula FVA = ![\frac{PMT}{r}[1-(1+r)^{-t} ]\\](https://tex.z-dn.net/?f=%5Cfrac%7BPMT%7D%7Br%7D%5B1-%281%2Br%29%5E%7B-t%7D%20%5D%5C%5C)
PMT= recurring payment = $300
r = discount rate; monthly rate in this case = 6% / 12 =0.5% or 0.005 as a decimal.
t = total duration ; 14 *12 = 168 months
Next, plug in the numbers into the FVA formula;
FVA = ![\frac{300}{0.005} [ 1-(1+0.005)^{-168} ]](https://tex.z-dn.net/?f=%5Cfrac%7B300%7D%7B0.005%7D%20%5B%201-%281%2B0.005%29%5E%7B-168%7D%20%5D)
FVA = 60,000 * 0.5673849
FVA = 34,043.0969
Therefore, Yolanda will have a balance of $34,043.10 in 14 years