Algebra 1.2

Starters

BTS(Back To School)

If B = 6, T = 3 and S = 8Then: B + T = 9 2S - B = 10 BTS = 144 S + S + S = 10T - BYou have four minutes to write down as many

equations as you can involving B, T and S.

C A R SWould you like to buy a car?

• The red car costs $5000 more than the blue car. • The green car is twice as expensive as the yellow car. • The blue car costs the same as the yellow car. If the green

and red cars cost the same, what is the total cost of all four cars?

ANSWER The cars cost:• Yellow $5000• Blue $5000• Red $10000• Green $10000• Total $30000

• Let the Blue car be $x.• The red car would then be Blue+$5000• Yellow cost $• Green cost $2X.• Green car is the same as Red car so we can write Green car= Red car

2x=x+$5000• solving this equation by the elimination method we have 2x-x=x-x+$5000

x=$5000So Blue car costs $5000Yellow Car costs $5000Green car costs $10000Red car costs $10000."

Christmas PresentsFive presents were bought for Christmas

The red and purple presents together cost $38The purple and blue presents together cost $40The blue and yellow presents together cost $33The yellow and green presents together cost $29The green and red presents together cost $36

What is the total cost of all five presents?

Answers

• The total cost of the five presents can easily be found by adding up the five costs given in the question then dividing by 2. Can you work out why?

• The answer is $88.• If you are interested, the individual presents

cost:• red = $19, purple = $19, blue = $21, yellow =

$12, green = $17.

Connecting Rules

• Give 20 rules connecting x and y• Eg. y - x = 1

X=3

Y=4

eQuation• Jamie thinks of a number which he types into

his calculator.• He then does the following operations:• Multiply by 4, subtract 5, multiply by 2 then add

5 (in that order).• He finds that the number he ends up with is 7

times his original number.• Form an algebraic equation to solve the

problem. What was Jamie's original number?

Answer

This question is best answered by forming an algebraic equation then solving it. Let Jamie's original number be x.

First operation gives 4xSecond operation gives 4x - 5Third operation gives 2(4x - 5)

Fourth operation gives 2(4x - 5) + 5This is equal to seven times the original number

2(4x - 5) + 5 = 7x8x - 10 + 5 = 7x

8x = 7x + 5x = 5

Jamie's original number was 5.

Online PsychicI know what you are thinking...

Think of a two digit number,*Reverse the digits to get another two digit number,

Subtract the smaller two digit number from the other,Add the digits of your answer together

(* The two digits must be different)

I know what your answer is! 9

Why? Explain algebraically

AB - BA = (Ax10+B)-(Bx10+A) = 9A-9B = 9(A-B)

Answer

Same Same

Jordan and Makayla are both the same age.Jordan multiplied his age by two, subtracted two

then multiplied the answer by five.Makayla multiplied her age by nine then added

threeJordan and Makayla arrived at the same answer as

each other.How old are Jordan and Makayla?

Answer

Let Jordan and Makayla be x years old.5(2x - 2) = 9x + 310x - 10 = 9x + 3x = 13Jordan and Makayla are both thirteen years old.

Sea ShellsWyatt and Vanessa collect sea shells. Wyatt

began a holiday with 207 shells and Vanessa began with 32 shells.

Each day of the holiday Wyatt found 38 shells and Vanessa found 63 shells on the beach. By the end of the holidays they had the same number of shells in total.

How long was the holiday?

Answer

Let the length of the holiday be x days.At the end of the holiday Wyatt had 207 + 38x

At the end of the holiday Vanessa had 32 + 63x32 + 63x = 207 + 38x

63x = 175 + 38x25x = 175

x = 7The holiday lasted seven days.

Simultaneous Occasions

David bought 6 clocks and 5 lamps which altogether cost $57.

On another occasion he bought 3 clocks and 10 lamps which cost $51.

What a bargain! How much does one clock cost? How much does one lamp cost?

Answer

• One clock costs $7.• One lamp costs $3.

Ratios and Algebra

The ratio of two numbers is 5 to 1. The sum is 18. What are the two numbers?

• Solution

Let x be the first number. Let y be the second number

x / y = 5 / 1

x + y = 18

Using x / y = 5 / 1, we get x = 5y after doing cross multiplication

Replacing x = 5y into x + y = 18, we get 5y + y = 18

6y = 18

y = 3

x = 5y = 5 × 3 = 15

As you can see, 15/3 = 5, so ratio is correct and 3 + 15 = 18, so the sum is correct.