# Heart of Algebra Simplifying, Problem Solving, Geometry

1. How many integers between 0 and 999 contain a single digit that is a 7?
2. The probability of scoring 90 or above is .35 in a group of 11 students, find the probability that 10 or 11 score a 90 or above?
3. In a bag there are 6 blue marbles, 4 red marbles, 7 yellow marbles, and 3 white marbles. How many which should be added so p(white) becomes 34?
4. Alan has 11 friends and is selecting 5 to come on a trip with him. How many ways can this be done?
5. 12 students run for Environmental Club Leadership Council which includes a President, Vice President, and Secretary. How many distinct Councils can be formed?
6. In a group of 8 girls and 4 boys, how many ways are there to select 2 boys and 2 girls?
7. abc is a randomly selected 3 digit integer from 100 to 999. Find the probability that abc contains exactly 1 digit that is an 8.
8. The Eagleneck gym has 6 bikes that 9 athletes want to use. At 5pm they randomly select one athlete per bike. If Alan, Bob, Caryn, Darrel, Edgar, and Frank are 6 of the athletes, find the probability that they are all selected.
9. The final price of a computer is C dollars. This is after a 15% off coupon, 8% sales tax and 4% employee discount. Find an expression for I, the initial price, in terms of the final price.
10. The final price of a TV is \$490 after a 9% tax and 18.25% discount. Find the original price.
11. Gender and Happiness are independent. The probability that a person is female is .5. The probability of being happy is .35. Find the probability that a randomly selected person is an unhappy male.
12. 17x-12y=14x+63y Find x/y.
13. 12x+34y=56x-78Find x/y.
14. 2(a+b)=5b Find a/b.
15. 10-10=0