1. A nursery offers orange and grapefruit trees for sale in two packages. One package consists of 3 orange trees and 4 grapefruit trees for $22. The other package contains 4 orange trees and 6 grapefruit trees for $31. Find the cost of an orange tree and a grapefruit tree. Show all your work.
2. The admission at a theater performance is $18 for an adult and $12 for a child. If a total of 700 tickets was sold and $10,800 was collected, how many children attended the performance? Show all your work.
3. Kathy invests $6000 in a bank. Part of her money is invested at 7% interest and part is invested at 9% interest. In one year Kathy earns $510 in interest. How much did she invest at each amount?
4. An airplane took 2 hours to fly 600 miles against a head wind. The return trip with the wind took hours. Find the speed of the plane in still air and the speed of the wind.
5. Two angles are complementary. The larger angle is more than eight times the measure of the smaller angle. Find the measure of the two angles. (Complementary angles are two angles whose sum is .)
6. The sum of the digits of a two-digit number equals of the number. If the digits of the number are reversed, the new number is equal to 36 less than the original number. Find the original number.