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  1.                                         :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