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Of quarts 60 x 60 x of sugar 20 0 5 amount of sugar

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Unformatted text preview: (B) No. of Pounds · x 30 x + 30 Price per Pound = 70 90 85 Total Value 70x 2700 85(x + 30) The original numerator was 4x, or 16. 2. (E) While this can be solved using the 5+ x 3 = , it is probably easier to 21 + x 7 equation 70 x + 2700 = 85 ( x + 30 ) 70 x + 2700 = 85 x + 2550 150 = 15 x x = 10 work from the answers. Try adding each choice to the numerator and denominator of which gives a result equal to 5 + 7 12 3 = = 21 + 7 28 7 3 . 7 5 to see 21 3. (D) No. of Pints Original 10 Added New 6 16 % of Acid .20 1.00 = Amount of Acid 2 6 8 3. (C) Here again, it is fastest to reason from the answers. Add 5 to each numerator and denominator to see which will result in a new fraction equal to 7 . 9 + 5 14 7 = = 15 + 5 20 10 10 Remember that 3 quarts of acid are 6 pints. There are now 8 pints of acid in 16 pints of solution. Therefore, the new solution is 1 or 50% acid. 2 4. (E) Here again, add 3 to each numerator and denominator of the given choices to see which will result in a new fraction equal to 2 . 7 + 3 10 2 = = 12 + 3 15 3 4. (A) 3 5. (C) Represent the original fraction by x . 2x No. of Quarts 60 x 60 + x · % of Sugar = 20 0 5 Amount of Sugar 1200 0 5(60 + x ) x+4 5 = 2x + 4 8 1200 = 5 ( 60 + x ) 1200 = 300 + 5 x 900 = 5 x x = 180 Cross multiply. 8 x + 32 = 10 x + 20 12 = 2 x x=6 5. (B) The original denominator is 2x, or 12. No. of Pounds 240 x 240 – x · % of Alcohol = 3 0 5 Amount of Sugar 720 0 5(240 – x ) Notice that when x quarts were evaporated, x was subtracted from 240 to represent the number of pounds in the mixture. 720 = 5 ( 240 − x ) 720 = 1200 − 5 x 5 x = 480 x = 96 www.petersons.com Problem Solving in Algebra 193 Exercise 7 1. (C) Slow Fast R x x+6 · T 3.5 3.5 = D 3.5x 3.5(x + 6) 4. (B) Going Return R 4 2 · T x 6–x = D 4x 2(6 – x ) The cars each traveled from 10 A.M. to 1 1:30 P.M., which is 3 hours. 2 He was gone for 6 hours. 4 x = 2 (6 − x ) 4 x = 12 − 2 x 6 x = 12 x=2 3.5x + 3.5(x + 6) = 287 Multiply by 10 to eliminate decimals. 35 x + 35 ( x + 6 ) =...
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This note was uploaded on 08/15/2010 for the course MATH a4d4 taught by Professor Colon during the Spring '10 term at Embry-Riddle FL/AZ.

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