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Sagot :
Miss, this problem of yours is an example of a direct proportion. Direct proportion can be easily identified when you think like this: If Gina takes more minutes typing, she can type more pages. If Gina types more pages, it will take her more minutes. That is a direct proportion. It is done like this:
Given:
30 minutes to type 3 pages
Asked: How many hours will it take her to type 63 pages at the same rate?
Solution:
30 minutes to type 3 pages can be written as: 30 : 3 or [tex] \frac{30}{3} [/tex]
The ratio of the asked hours and the 63 pages is: ? : 63 or we can use a variable to represent the question mark, we use x and it becomes x : 63 or [tex] \frac{x}{63} [/tex]
So it is:
[tex] \frac{30}{3} [/tex] [tex] \frac{x}{63} [/tex]
In this one, what did you observe? After displaying the ratios that we transformed into fractions, we cross multiply them. Take note that 30 and x are horizontally aligned because they are both "time." 3 and 63 are aligned because they are both pages. So we continue:
[tex] \frac{30}{3} [/tex] [tex] \frac{x}{63} [/tex] (cross multiply: 30 x 63 and 3 times x)
63 x 30 = 3x (it becomes)
1, 890 = 3x ( in this one, how to find the value of x? Just divide 1, 890 by 3 and that will be x and our answer.)
1, 890 = 3x
1, 890 / 3 = x
630 = x
Check:
[tex] \frac{30}{3} \frac{x}{63} [/tex] ( substitute x for 630)
[tex] \frac{30}{3} [/tex] [tex] \frac{630}{63} [/tex]
(cross multiply, if their products are the same, it means 630 is correct)
[tex] \frac{30}{3} \frac{630}{63} [/tex]
30 x 63 = 630 x 3
1, 890 = 1, 890, they are the same! That means, 630 is correct!
We are not yet done! Take note of the units! 630 is not yet the final answer because remember! It is in minutes! The question asks for hours! So to convert it into hours, we divide it by 60 because there are 60 minutes in 1 hour!
630 minutes ⇒ hours
630 minutes / 60 = 10 . 5 or 10 [tex] \frac{1}{2} [/tex] hours
(but, if you want it to be complete, this is the original equation)
630 minutes ⇒ hours
630 minutes x [tex] \frac{1 hour}{60minutes} [/tex]
= 630 x [tex] \frac{1}{60} [/tex] ( the minutes are cancelled that is why they are not there.)
= [tex] \frac{630}{60} [/tex] = 10 [tex] \frac{1}{2} [/tex] hours
Answer:
10 [tex] \frac{1}{2} [/tex] hours
Given:
30 minutes to type 3 pages
Asked: How many hours will it take her to type 63 pages at the same rate?
Solution:
30 minutes to type 3 pages can be written as: 30 : 3 or [tex] \frac{30}{3} [/tex]
The ratio of the asked hours and the 63 pages is: ? : 63 or we can use a variable to represent the question mark, we use x and it becomes x : 63 or [tex] \frac{x}{63} [/tex]
So it is:
[tex] \frac{30}{3} [/tex] [tex] \frac{x}{63} [/tex]
In this one, what did you observe? After displaying the ratios that we transformed into fractions, we cross multiply them. Take note that 30 and x are horizontally aligned because they are both "time." 3 and 63 are aligned because they are both pages. So we continue:
[tex] \frac{30}{3} [/tex] [tex] \frac{x}{63} [/tex] (cross multiply: 30 x 63 and 3 times x)
63 x 30 = 3x (it becomes)
1, 890 = 3x ( in this one, how to find the value of x? Just divide 1, 890 by 3 and that will be x and our answer.)
1, 890 = 3x
1, 890 / 3 = x
630 = x
Check:
[tex] \frac{30}{3} \frac{x}{63} [/tex] ( substitute x for 630)
[tex] \frac{30}{3} [/tex] [tex] \frac{630}{63} [/tex]
(cross multiply, if their products are the same, it means 630 is correct)
[tex] \frac{30}{3} \frac{630}{63} [/tex]
30 x 63 = 630 x 3
1, 890 = 1, 890, they are the same! That means, 630 is correct!
We are not yet done! Take note of the units! 630 is not yet the final answer because remember! It is in minutes! The question asks for hours! So to convert it into hours, we divide it by 60 because there are 60 minutes in 1 hour!
630 minutes ⇒ hours
630 minutes / 60 = 10 . 5 or 10 [tex] \frac{1}{2} [/tex] hours
(but, if you want it to be complete, this is the original equation)
630 minutes ⇒ hours
630 minutes x [tex] \frac{1 hour}{60minutes} [/tex]
= 630 x [tex] \frac{1}{60} [/tex] ( the minutes are cancelled that is why they are not there.)
= [tex] \frac{630}{60} [/tex] = 10 [tex] \frac{1}{2} [/tex] hours
Answer:
10 [tex] \frac{1}{2} [/tex] hours
It will take 10 1/2 hours will it take her to typre 63 pages at the same rate.
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