SOLUTION: 1. Solve the following simple interest word problem:
Sue, a recent retiree, requires $6,000 per year in extra income. She has $50,000 to invest and can invest in B-rated bonds
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Question 739904: 1. Solve the following simple interest word problem:
Sue, a recent retiree, requires $6,000 per year in extra income. She has $50,000 to invest and can invest in B-rated bonds paying 15% per year or in a certificate of deposit (CD) paying 7% per year. How much money should be invested in each to realize exactly $6,000 in interest per year?
2. Solve the following time-distance word problem:
A motorboat heads upstream a distance of 24 miles on a river whose current is running at 3 miles per hour (mi/hr). The trip up and back takes 6 hours. Assuming that the motor boat maintained a constant speed relative to the water, what was its speed?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Part I 15.00% per annum ------------- Amount invested =x
Part II 7.00% per annum ------------ Amount invested = y
50000
Interest----- 6000.00
Part I 15.00% per annum ---x *
Part II 7.00% per annum ---y
Total investment
x + 1 y= 50000 -------------1
Interest on both investments
15.00% x + 7.00% y= 6000
Multiply by 100
15 x + 7 y= 600000.00 --------2
Multiply (1) by -15
we get
-15 x -15 y= -750000.00
Add this to (2)
0 x -8 y= -150000
divide by -8
y = 18750 - x)
Part I 15.00% $ 31250
Part II 7.00% $ 18750
CHECK
31250 --------- 15.00% ------- 4687.50
18750 ------------- 7.00% ------- 1312.50
Total -------------------- 6000.00
------------
Boat speed x mph
current speed 3 mph
Distance with wind 24 miles
Distance against wind 24 miles
spee with current x + 3 mph
speed against x 3 mph
Total time = 6 hours
Time with current= 24 /( x + 25 )
time against current 24 / ( x -25 )
Time with current + time against = 10 hours
24 /( x + 3 ) + 24 /(x -3 ) = 6
LCD = ( x + 3 )* (x -3 )
multiply the equation by the LCD
we get
24 * (x -3 )+ 24 (x + 3 )= 6 (x^2- 9 )
24 x -72 + 24 x + 72 )= 6 X^2 54
48 x 0 = 10 X^2 -54
6 X^2 -48 x 0 + -54 = 0
6 X^2+ -48 x+ -54 = 0 OK
/ 1
6 X^2 -48 x -54 = 0
Find the roots of the equation by quadratic formula
a= 6 b= -48 c= -54
b^2-4ac= 2304 - -1296
b^2-4ac= 3600 = 60 =
x1=( 48 + 60 )/ 12
x1= 9
x2=( 48 -60 ) / 12
x2= -1
Ignore negative value mph
x = 9
m.ananth@hotmail.ca
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