Answer:
The teacher can purchase 61 pencils with $5
Step-by-step explanation:
This is a simple proportion problem. It can be solved by pure logic reasoning without any formulas
It a dozen pencils cost $0.97, each pencil cost $0.97/12=0.08083
With $5 she will be able to purchase 5/0.08083=61.85 pencils
We must round to the nearest lower integer
The teacher can purchase 61 pencils with $5
f = (f1 f2) / (f1 + f2)
f(f1 + f2) = f1 f2
f f 1 + f f 2 = f1 f 2
f1 f2 - f f2 = f f1
f2 (f1 - f) = f f1
f2 = (f f1) / (f1 - f) <==== solution
Answer:

Step-by-step explanation:
We have been given that there are total 9 people who entered the drawing competition. There are 3 prizes to be distributed to the winners. The total number of ways that 3 prizes can be awarded to the 9 people can be determined as 9*8*7 = 504.
The total number of ways in which I win the first prize and my mom wins the second prize would be 1*1*7 = 7.
Therefore, the probability that I win the first prize and my mom wins the second prize would be: 
Answer:
1 to 200 or 1:200 or 1/200
Step-by-step explanation:
If there is 1 shark for every 200 fish then the ratio would be sharks (1) over fish (200)