:Q 1. How many pints of water should be added to 10 pints of a 90% solution of alcohol to reduce it to a 75% solution? (a) 10 (b) 5 (c) 2 (d) 0 (e) 4 :RCC 1. (c) 2 Ans. original new water solution solution ---------------------------- % alcohol 0% 90% 75% ---------------------------- amount y 10 10 + y ---------------------------- solution 0y .90(10) .75(10 + y) 9 = .75(10 + y) 9 = 7.5 + .75y 1.5 = .75y (multiply by 100) 150 = 75y y = 2 pints Ans. :RA :Q 2. How many ounces of pure gold should be added to 15 ounces of a 20% alloy of gold to produce 14 carat gold? (14 carat gold means 14 parts gold to 10 parts of other metal). (a) 13 4/5 (b) 12 3/4 (c) 13 (d) 0 (e) 13 5/8 :RCA 2. (a) 13 4/5 Ans. original new gold alloy alloy ----------------------------- % gold 100% 20% 58 1/3% ----------------------------- amount y 15 15 + y ----------------------------- alloy y 1/5 (15) 7/12 (15 + y) 7 y + 3 = -- (15 + y) 12 12y + 36 = 105 + 7y multiply by 12 and clear parenthesis 5y = 69 y = 13 4/5 Ans. :RA :Q 3. How many pounds of tea worth .90 a pound should be mixed with 15 pounds of tea worth .40 a pound to make a blend worth .60 a pound? (a) 5 lb. (b) 20 lb. (c) 1 lb. (d) 10 lb. (e) 0 lb. :RCD 3. (d) 10 lb. Ans. cost number total per lb. of lb. cost ------------------------------ tea a .90 y .90y ------------------------------ tea b .40 15 6.00 ------------------------------ blend .60 15 + y .60(15 + y) 90y + 600 = 60(y + 15) 90y + 600 = 60y + 900 30y = 300 y = 10 lb. Ans. :RA :Q 4. Tickets for the Senior Play were .35 for students and $1.00 for adults. If 200 tickets were sold and the total receipts were $148.00, how many adults attended? (a) 140 (b) 80 (c) 120 (d) 60 (e) 100 :RCC 4. (c) 120 Ans. cost total each number cost ---------------------------- students .35 y .35y ---------------------------- adults 1.00 200 - y 1.00(200 - y) ---------------------------- total .74 200 $148.00 35y + 20000 - 100y = 14800 -65y = -5200 y = 80 students 200 - y = 120 adults. Ans. :ET :ET
