Three roommates-Bela, Gyorgy, and Janos-together saved money for a trip. The amount that Bela saved was equal to 8% of his monthly income. The amount that Gyorgy saved was exactly ~$1 \over 3$~ of the total amount saved by all 3 roommates. what was the total amount saved for the trip by all 3 roommates?

1. Bela had a monthly income of $2,000

2. Janos saved 1.5 times as much for the trip as Bela

If a and b are constants, is the expression ~$x+b \over \sqrt{x+a}$~ defined for x=-2?

1.a=5

2.b=6

A paint mixture was formed by mixing exactly 3 colors of paint. By volume, the mixture was x% blue paint, y%  green paint, and z%  red paint. If exactly 1 gallon of blue paint and 3 gallons of red paint were used, how many gallons of green paint were used?

1.~$x=y$~

2.~$z=60$~

In the figure above, PQRT is a rectangle. what is the length of segment PQ?

1. The area of region PQRS is 39 and TS=6

2. The area of region PQRT is 30 and QR=10

If ~$x$~ and ~$y$~ are the lengths of the legs of a right triangle, what is the value of ~$xy$~?

1. The hypotenuse of the triangle is 10 ~$\sqrt{2}$~

2. The area of the triangular region is 50

If each side of parallelogram ~$P$~ has length 1, what is the area of ~$P$~ ?

1. One angle of ~$P$~ measures 45 degrees.

2. The altitude of ~$P$~ is  ~$\frac{\sqrt{2}}{2}$~.

If ~$a$~ and ~$b$~ are integers, is ~$a^5 < 4^b$~ ?

1. ~$a^3 = -27$~

2. ~$b^2 = 16$~

The total price of 5 pounds of regular coffee and 3 pounds of decaffeinated coffee was $21.50. What was the price of the 5 pounds of regular coffee?

1. If the price of the 5 pounds of regular coffee had been reduced 10 percent and the price of the 3 pounds of decaffeinated coffee had been reduced 20 percent, the total price would have been 18.45.

2. The price of the 5 pounds of regular coffee was S3.50 more than the price of the 3 pounds of decaffeinated coffee.

What number is 6 more than ~$x + y$~?

1. ~$y$~ is 3 less than ~$x$~.

2. ~$y$~ is twice  ~$x$~.

Jack picked 76 apples. Of these, he sold ~$4y$~ apples to Juanita and ~$3t$~ apples to Sylvia. If he kept the remaining apples, how many apples did he keep?(~$t$~ and ~$y$~ are positive integers.)

1. ~$y ≥ 15$~ and ~$t$~ = 2

2. ~$y = 17$~