# 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 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%)