TIU CET Review Math Session 5

WORD PROBLEMS

TIU College Entrance Test Review

Math Session 5

PRB / Fractions Example (Not in the book)

3 Methods:

1. By drawing

2. By PRB method (Percentage-Rate-Base)

3. By Algebra

2 1What part of is ?

3 6

23161

Answer : 4

Method 2: PRB triangle

2 1What part of is ?

3 6

Pr

B

1623

r

1 36 2

r

14

r

Method 3: By Algebra

2 1What part of is ?

3 6N 1

6

23

=

2 1

3 6N

32

32

214

N

Fractions Example 2 (Not in the book)

Answer: 16.

How many halves are in 8?

18

2

12

28

1 16

Defined Operations(Example not in the book)

The word problem will use a symbol / character to define an operation / process.

If A B = A - B, then what is 3 8 ?

3 8 3 8 5 What to do:

Use the given formula in the problem to solve.

Rational Exponents / Radicals (This example not in the book)

RECALL:

231

Find .64

nm mnb b

12 31

64

Is ?mn nmb b YES!

2131

We can also say: 64

231

Find .64

2131

64

Just getting the cube root.

13 3

Recall:

y y

2131

64

2

31

= 64

21

= 4

1 =

16

p.76 Ex. 3 NUMBER PROBLEM

The sum of three consecutive even integers is 66. What is the largest number?

___ ___ ___ 66 2 4 66x x x

3 6 66x 3 60x

20x The largest

is 24.

Ex. 21 p. 83 Motion Problem

Ross and Rachel agree to meet for a date. Ross drives at 40 kph and Rachel at 35 kph. After how many hours will they meet if they are 150 km apart and they start driving directly toward each other at the same time?

1.) Make a diagram/illustration of the scene.

2.) Make a table of the given.

Let t = number of hours until they meet= time Ross traveled = time Rachel

DiagramRoss, 40kph

Rachel, 35 kph

150 km

We use the formula, distance = rate x time

40 35 150tt

distance distance 150Ross Rachel

150Ross Ross Rachel Rachelrate time rate time

p. 87 Ex. 29 MIXTUREHow much water must be added to 100 L of denatured alcohol 90% pure to dilute into 75% alcohol content?

100 L

90 %

X

0%

100 + X

75%

p. 88 Ex. 32 MONEY

A scholarship trust fund has P65,000 in capital. Some of the money is invested in a bank at an annual interest rate of

and the rest at 6%. If the

income from the amount invested at

exceeds the investment at 6% by P300 after one year, how much is invested at each rate?

14 %

2 14 %

2

MoneyP65,000

14 %

26%

Interest at 4.5% = 4.5%xInterest at 6% = 6% (65,000 – x)

Let x = money invested at 4.5%

Equation?

p. 88 Ex. 32 MONEY

A scholarship trust fund has P65,000 in capital. Some of the money is invested in a bank at an annual interest rate of

and the rest at 6%. If the

income from the amount invested at

exceeds the investment at 6% by P300 after one year, how much is invested at each rate?

14 %

2 14 %

2

“…income from the amount invested at exceeds the investment at 6% by P300 after one year.”• .

Interest Principal Rate Time

I PRT

4.5% 6%(65,000 ) 300x x

Interest at 4.5% : 4.5%xInterest at 6% : 6% (65,000 – x)

14 %

2

Note: If time is more than one year or investment period:

Geometry Example 1 (Not in the book)

The edge of a cube is doubled. What happens to its volume?

3cubeV e 32newV e

38newV e

Volume increases 8 times bigger.

GEOMETRY Example (Not in the book)An architect is to design a swimming pool in a hotel, to be fenced off on 3 sides with 60 meters of material. The pool is to have an area of 352 sq.m.

What should the dimensions of the pool be?

L W

60 2W L

352 LW

60 2W L 352 LW

System of Equations: Perimeter

Area

Let’s use SUBSTITUTION METHOD:-Represent L in terms of W.-Substitute into 2nd equation.

60 2W L 352 60 2W W

352 60 2W W 2352 60 2W W

Can we isolate the variable W above?

The equation above is NOT linear. It is A QUADRATIC equation. (Degree of x is 2)

How can we solve for W?

Page 603 Methods to solve Quadratic Equations:

• 1.) FACTORING

• 2.) COMPLETING THE SQUARE

• 3.) QUADRATIC FORMULA

Factoring2352 60 2W W