Help on these problems would be appreciated!
1) Loan X has a principal of 10000x and simple annual interest of 4%. Loan Y has a principal of 10000Y and simple annual interest of 8%. Both loans will be consolidated into loan Z, where the principal is (10000x+10000y) and simple interest is r%, where r=(4x+8y)/(x+y). What are x and y for r=.05? ANSWERS: x=96, y=32
2) What is the value of x? 2^x - 2^(x-2) = 3*(2^13)
ANSWER: X=15
3) 6 machines work at the same constant rate and it takes them 12 days to complete 1 job. If the job must be done in 8 days, how many machines should be added?
ANSWER: 3
4) (Similar as above) Each of 10 machines works at the same constant rate. Together they complete a job in 16 hours. How many hous does it take 8 machines to finish the job?
ANSWER: 20
5) The number of stamps Kyle had and the number of stamps Amy had were in a ratio of 5:3 respectively. After Kyle gave Amy 10 stamps, the ratio changed to 7:5. As a result of the gift, Kyle had how many more stams than Amy?
ANSWER: 40
6) Codes can be formed by 1, 2 or 3 letters from the 26-letter alphabet. If letters can be repeated and if the same letters in different order are taken as different codes, then how many codes can be formed?
ANSWER: 18278
7) For all 1<=k<=10, the kth term of a sequence is (-1)^(k+1) * (1/2^k). If T is the sum of the first 10 terms in the sequence, then T is
a) Greater than 2
b) Between 1 and 2
c) Between 0.5 and 1
d) Between .25 and .5 (right answer)
e) Less than .25
1) Loan X has a principal of 10000x and simple annual interest of 4%. Loan Y has a principal of 10000Y and simple annual interest of 8%. Both loans will be consolidated into loan Z, where the principal is (10000x+10000y) and simple interest is r%, where r=(4x+8y)/(x+y). What are x and y for r=.05? ANSWERS: x=96, y=32
2) What is the value of x? 2^x - 2^(x-2) = 3*(2^13)
ANSWER: X=15
3) 6 machines work at the same constant rate and it takes them 12 days to complete 1 job. If the job must be done in 8 days, how many machines should be added?
ANSWER: 3
4) (Similar as above) Each of 10 machines works at the same constant rate. Together they complete a job in 16 hours. How many hous does it take 8 machines to finish the job?
ANSWER: 20
5) The number of stamps Kyle had and the number of stamps Amy had were in a ratio of 5:3 respectively. After Kyle gave Amy 10 stamps, the ratio changed to 7:5. As a result of the gift, Kyle had how many more stams than Amy?
ANSWER: 40
6) Codes can be formed by 1, 2 or 3 letters from the 26-letter alphabet. If letters can be repeated and if the same letters in different order are taken as different codes, then how many codes can be formed?
ANSWER: 18278
7) For all 1<=k<=10, the kth term of a sequence is (-1)^(k+1) * (1/2^k). If T is the sum of the first 10 terms in the sequence, then T is
a) Greater than 2
b) Between 1 and 2
c) Between 0.5 and 1
d) Between .25 and .5 (right answer)
e) Less than .25
