Question: 67
INVESTMENTS
Answer:
Assume X = amount in stocks
Inheritance amount= 24,000
Advisor’s recommended ratio = 3/5
Based on the provided data; formulated the following equation
24000=3/5 multiply by x+ x
24000= 8/5 (x) and by further arranging the like terms of the equation we get
24000* 5/8+ x or x= 24000* 5/8
And therefore x=15000
Checking the answers:
Assessing the validity of the answer requires putting the estmated amount of x in the initial equation.
24,000=3/5 (15,000) + (15,000)
By calculating this, it becomes evident that LHS is equal to RHS
24,000=24,000
And therefore the answer is true. And 15,000 subtracted from 24,000 makes it 9000 that should be invested in bonds. According to the calculation it is recommended to invest 15,000 in stocks and 9000 in bonds.
Question 71:
BANKING
Answer:
For this loan problem let the fraction (f) of 500,000 dollars be loaned at 6 percent meanwhile for the rest of it be 1-f at 11 percent per annum. Therefore the total interest is:
6/100*500,000(f) + (1+f) * 500,000 *11/100 = 30000(f) and
30,000(f) + 55,000(1-f) = 55,000 so
55000-25,000(f) = 43750
For this reason 25,000(f) = 11,250 and/or f=45/100=0.45
Therefore the amount loaned at 6% is the:
500,000(f) = 225,000
Question 73:
INVESTMENTS
Answer:
Let’s suppose x= amount to be invested at 5%
And the investment amount at 9% is x-25,000
In this context the sum of interest earned is:
0.05*x + 0.09 * (25,000-x) =1,875
0.05*x + 2,250-0.09*x =1,875 so
-0.04*x =-375
X= 9,375
Therefore, 9,375 dollars are the amount to be invested at 5%
Checking answer:
0.05*9,375+0.09*15625=468.75 and
468.75+ 1406, 25 = 1,875
Question 76:
CANDY
Assume
x= numbers of pounds almonds = 40 Ibs
Y= numbers of pounds peanuts =10 Ibs
And therefore we get the equation:
X=50-y
By arranging the equation:
X+y = 50
6.50(x) + 4.00(y) = 6.00 (50)
And by suing substitution:
X=y = 50
6.50x+ 4(y) = 300
6.50 (50-y) + 4(y) =300
325-6.50y+4(y)=300
325-2.50y=300
-2.50(y) =-25
And therefore
Y= 10
By putting the value of y in the equation we get:
X+10=50
X=40
Question 77
COINS
X= number of quarters
Y= number of dimes
X+y = 47
And y=47-x
Therefore .25+.10y=9.50
.25x+.10(y) =9.50
.25x+4.7-.10x=9.50
.15(x) + 4.7= 9.50
-4.7-4.70
.15(x)/.15= 4.8/.15
X=32
Y = 47-32
In this way the value of y becomes
Y=15
That’s makes it evident that bobby has 15 dimes and 32 quarters.
Question 89
ANTIFREEZE
Let’s suppose V= volume of antifreeze (40%)
And 15-V=volume of pure antifreeze (100%) required
It is evident that last antifreeze composition was 15 litre of antifreeze (50%).
For this situation save V 40% antifreeze liters and combine it with 15-V 100% antifreeze liters. For this purpose:
40% (V) =100% (15-V) = 50% (15)
To convert the percentage
0.4 V + 1.0 (V-15) = 0.5 (15) so
.4 V + 1.0 (15)-1.0 V =7.5
By combining the like terms:
.4(v) – 1.0 (v) +15=7.5
-0.6(v)+15 =7.5
-0.6(v) =7.5-15
-0.6(v) -7.5
V=12.5 litre of anitfreeze (40%)
15-v= 2.5 liter of antifreeze pure(100%)
