If you have Mr Laurence for ALG 278 Do problem Numbers 1 – 5. If you have Mr Laurence for honors algebra do problem numbers 6 – 14. DO NOT WRITE ON THIS 1) A music store sells two types of compact discs. The first type sells for $7.50 and the second type sells for $11.50. You buy a total of 12 compact discs and spend $110. How many of each type of compact disc did you buy? 2) 350 tickets are sold to a high school basketball game. Some are student tickets, which cost $3 and some are adult tickets, which cost $5. If $1,450 is collected from ticket sales, determine how many of each type of ticket were sold. 3) An ice cream shop sells ice cream in two different sized cups, a 5-­‐ounce cup which costs $2.50 and an 8-­‐ounce cup which costs $4.00. One hot summer day a total of 75 cups were sold for a total of $252. How many of each type of cup were sold? 4) How many liters of pure acid should be mixed with 80 liters of 40% acid in order to produce a 65% acid? 5) The perimeter of a rectangle is 30 cm. The length of the rectangle is twice the width. What are the length and width of the rectangle? Helpful formulas: Perimeter 2L + 2W = P 6) Find the equation of lines that are parallel and perpendicular to 4x – 3y = 8 and that pass through the point (12, -­‐ 5). 7) Find the equation of lines that are parallel and perpendicular to x = 4 and that pass through the point (3, 5). 8) Find the equation of lines that are parallel and perpendicular to y = –2 and that pass through the point (4, -­‐ 3). 9) Solve by Factoring: x8 – 1 = 0 10) Find the vertex using the completing the square method: y = 2x2 + 12x − 1 11) Find the vertex using the completing the square method: y = 3x2 − 6x + 5 12)Find the vertex using the completing the square method: y = −5x2 − 25x + 6 13) Find the vertex using the completing the square method: y = −2x2 + 8x − 3 14)Find the vertex using the completing the square method: y = −4x2 + 24x + 1 ANSWER KEY 1) 5 of the $11.50 cds and 7 of the $7.50 cds. 2) 150 student tickets and 200 adult tickets 3) 32 5-­‐ounce cups and 43 8-­‐ounce cups were sold 4) approximately 57.1 liters of pure acid 5) the length is 10 cm and the width is 5 cm !
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6) parallel: y = ! 𝑥 − 21 perpendicular: y = − ! 𝑥 + 4 7) parallel: x = 3 perpendicular: y = 5 8) parallel: x = 4 perpendicular: y = – 3 9) (x4 + 1)(x2 + 1)(x+1)(x – 1); only 2 real solutions x= 1 and x = -­‐1 10) y = 2(x + 3)2 – 19 ; vertex is at (-­‐3, -­‐ 19) 11) y = 3(x – 1)2 + 2 ; vertex is at (1, 2) !
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12) y = – 5(x + !)2 + 37! ; vertex is at (–2!, 37!) 13) y = –2(x – 2)2 + 5 ; vertex is at (2, 5) 14) y = –4(x – 3)2 + 37 ; vertex is at (3, 37)