Algebra Questions And Answers

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 estimated 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 is 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

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 using 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 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 the last antifreeze composition was 15 liters 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%)