1. Word Problems There were originally twice as many boys as girls in my Honors Geometry class. After three new girls join the class, the total number of students is 24. How many boys and girls were originally in the class? Let original number of boys = y original number of girls = x y = 2x x+3 +y = 24 x=7 and y=14 There were originally 7 girls and 14 boys in the class.

2. Coin Problem Patrick has only quarters and dimes in his piggy bank. There are currently 26 coins in the bank. If he adds 7 quarters and 3 dimes, the total value of the coins will be $7.35. Find the number of quarters and the number of dimes Patrick originally had in the bank. Let d = original number of dimes and q = original number of quarters d + q = 26 0.10(d + 3) + 0.25(q + 7)= 7.35 q = 18 quarters d = 8 dimes

3. Wind/Current Problem If a plane flies into the wind, its maximum speed is 450 mph. If a plane travels with the wind, its maximum speed is 520 mph. What is the maximum speed of the plane in still air, and what is the speed of the wind? Let s= speed of the plane and w = speed of the wind s – w = 450 s + w = 520 w= 35 mph s = 485 mph

4. Wind/Current Problem An airplane flying into a head wind travels the 1800-mile flying distance between two cities in 3 hours and 36 minutes. On the return flight, the same distance is traveled in 3 hours. Find the ground speed of the plane and the speed of the wind, assuming that both remain constant. [Ground speed is the speed of the plane if there were no wind.] Let r = ground speed of the plane and w = speed of the wind Distance = rate * time Answer: The ground speed of the plane is 550 miles per hour and the wind speed is 50 miles per hour. Rate (mph) Time (hours) Distance (miles) Trip there Return trip

5. Wind/Current Problem An airplane flying into a head wind travels the 1800-mile flying distance between two cities in 3 hours and 36 minutes. On the return flight, the same distance is traveled in 3 hours. Find the ground speed of the plane and the speed of the wind, assuming that both remain constant. [Ground speed is the speed of the plane if there were no wind.] Let r = ground speed of the plane and w = speed of the wind Distance = rate * time Answer: The ground speed of the plane is 550 miles per hour and the wind speed is 50 miles per hour. Rate (mph) Time (hours) Distance (miles) Trip there Return trip

6. Age Problem In six years, Sarah will be twice as old as Mary. Sarah is currently five times as old as Mary. How old are Sarah and Mary now? Mary is currently 2 years old and Sarah is ten years old.