9514 1404 393
Answer:
11) x = 9
12) x = 9
Step-by-step explanation:
11) Corresponding segments are proportional, so ...
x/6 = 12/8
x = 6(12)/8 . . . multiply by 6
x = 9
__
12) Similar triangle relationships show you the geometric mean relationship that applies in this case.
long side/short side = x/3 = 27/x
x² = 3·27 . . . . . . cross multiply
x = √(3·27) . . . . geometric mean relationship
x = 9
It will take her 8 weeks to have enough money for a bike. I made the equation 125+15x=245 and multiplied 15 by 8 to get exactly 245
X=4 and y=6
For this, you should use simultaneous equations
Current amount in account
P=36948.61
Future value of this amount after n years at i=11% annual interest
F1=P(1+i)^n
=36948.61(1.11)^n
Future value of $3000 annual deposits after n years at i=11%
F2=A((1+i)^n-1)/i
=3000(1.11^n-1)/0.11
We'd like to have F1+F2=280000, so forming following equation:
F1+F2=280000
=>
36948.61(1.11)^n+3000(1.11^n-1)/0.11=280000
We can solve this by trial and error.
The rule of 72 tells us that money at 11% deposited will double in 72/11=6.5 years, approximately.
The initial amount of 36948.61 will become 4 times as much in 13 years, equal to approximately 147800 by then.
Meanwhile the 3000 a year for 13 years has a total of 39000. It will only grow about half as fast, namely doubling in about 13 years, or worth 78000.
Future value at 13 years = 147800+78000=225800.
That will take approximately 2 more years, or 225800*1.11^2=278000.
So our first guess is 15 years, and calculate the target amount
=36948.61(1.11)^15+3000(1.11^15-1)/0.11
=280000.01, right on.
So it takes 15.00 years to reach the goal of 280000 years.