Sarah can type 225 words in five minutes. She then typed 135 words in three minutes. If sarah types for 24 minutes, how many words did she type?
A. What is the answer? (I answered 1080)
B. Explain what the constant of variation is in the problem. Write an equation for the problem.
C. What is a constant of variation?
first rate = 225/5 words per minute = 45 words/min
2nd rate = 135/3 words per min = 45 words/min
ahhh, the same rate
so words typed = 24(45) or 1080 words
A. The answer is 1080 words.
B. The constant of variation in this problem is the rate at which Sarah types, which we can represent as "w" words per minute. We can use this equation to calculate the number of words Sarah types in a given amount of time:
w = k * t
Where:
w = Number of words typed
k = Constant of variation
t = Time in minutes
In the first scenario, she types 225 words in 5 minutes, so we can set up the equation as follows:
225 = k * 5
Solving for k, we get:
k = 225 / 5
k = 45
Now, using this value of k, we can find the number of words Sarah types in the second scenario, where she types 135 words in 3 minutes:
135 = k * 3
Substituting the value of k:
135 = 45 * 3
Finally, we can calculate the number of words Sarah types in 24 minutes:
w = k * t
w = 45 * 24
w = 1080
Therefore, Sarah typed 1080 words in 24 minutes.
C. The constant of variation, also known as the constant of proportionality, is a value that relates two variables in a proportional relationship. It determines how the variables change in relation to each other. In this problem, the constant of variation represents the rate at which Sarah types words per minute. It remains constant because the rate at which she types does not change.