1. How many cups of grapefruit juice must be added to 30 cups of punch containing 8% grapefruit juice to obtain a punch that is 10% grapefruit juice?
2. Find the selling price per ounce of a face cream mixture made from 70 oz of a face cream that costs $4 per oz, and 30 oz of a face cream that costs $15 per oz
3. The units of digit of a two-digit number is one more than four times the ten digit. The number formed by reversing the digits is 63 larger than the original number. Find the original number.
4. Find the solution set for 2 - 3x < 8 and (intersect) 2x - 3 -9 (a. { x | -2 < x -3 b. { x | x < -2 } { x | x -3 } c. { x | x < -2 } d. { x | x > -2 }
5. An investment of $5,000 is made at an annual simple interest rate of 8.5%. How much additional money must be invested at an annual simple interest rate of 11.8% so that the total interest earned is 9.8% of the total investment?
6. A motorboat traveling with the current went 45 miles in 3 hours. Against the current, it took 4.5 hours to travel the same distance. Find the rate of the boat in calm water.
7. One solution contains 20% alcohol and another solution contains 60% alcohol. Some of each of the two solutions is mixed to produce 10 liters of a 50% solution. How many liters of the 60% solution should be used?
8. A stamp collection consists of 5 cent, 8 cent, and 13 cent stamps. The number of 13 cent stamps is one more than twice the number of 5 cent stamps. The number of 13 cent stamps is six more than the number of 8 cent stamps. The total value of all the stamps is $5.37. Find the number of 5 cent stamps.
9. Maximize z = 3x + y subject to 2x + y 8, 2x + 3y 12, x 0, y 0
10. Minimize z = x + y subject to y = 2, x 0, y 0