Algebra 1.2 Starters

BTS (Back To School) If B = 6, T = 3 and S = 8 Then: B + T = 9 2S - B = 10 BTS = 144 S + S + S = 10T - B You have four minutes to write down as many equations as you can involving B, T and S.

C A R S Would 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=$5000 So Blue car costs $5000 Yellow Car costs $5000 Green car costs $10000 Red car costs $10000."

Christmas Presents Five presents were bought for Christmas The red and purple presents together cost $38 The purple and blue presents together cost $40 The blue and yellow presents together cost $33 The yellow and green presents together cost $29 The 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.

X=3 Y=4 Connecting Rules Give 20 rules connecting x and y Eg. y - x = 1

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 4x Second operation gives 4x - 5 Third operation gives 2(4x - 5) Fourth operation gives 2(4x - 5) + 5 This is equal to seven times the original number 2(4x - 5) + 5 = 7x 8x - 10 + 5 = 7x 8x = 7x + 5 x  = 5 Jamie's original number was 5.

Online Psychic I 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

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

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 three Jordan 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 + 3 Jordan and Makayla are both thirteen years old.

Sea Shells Wyatt 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 + 63x 32 + 63x = 207 + 38x 63x = 175 + 38x 25x = 175 x = 7 The 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 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.