EVALUATE
identity the base, rate, and percentage. Then, find the value of the unknown.
Base
Rate
Percentage
Given
30% of n is 1.8
240 is n% of 400
2.4 is 30% of n
225 is 25% of n
70% of nis 14.7
113 is 13% of n
28% of n is 196
35% of n is 1200
175.5 is 11% of n
n is 40% of 65
Answer:
(see explanation)
Step-by-step explanation:
Percentage is the value that is part of the base.
Base is the value that represents the 100%, or the total value.
Rate is the value that defines what the percentage is part of the base.
Percentage, base and rate are related with the equation:
[tex]p=br[/tex]
where p is the percentage, b is the base, r is the rate.
solving for the other variables in terms of the other gives us:
[tex]b = \frac{p}{r} \\\\r = \frac{p}{b}[/tex]
Usually it is better to change the rate to its equivalent fraction or decimal form.
To identify which is which on a problem here are some keywords:
- The rate is almost always a value with the percentage sign (%), or in fraction or decimal.
- The base is larger than the percentage if the rate is less than 100%.
- The number that follows the word “of” is usually the base, since “of” means “part of a whole”.
Let’s go to your questions
- 30% of n is 1.8
30% is the rate, n is the base, so 1.8 is the percentage. We are looking for the base. We use the formula:
[tex]b = \frac{p}{r} \\\\b = \frac{1.8}{0.3} \\\\b = \frac{18}{6}\\\\b = 3[/tex]
n is 3.
- 240 is n% of 400.
n% is the rate, 400 is the base since it follows “of”, so 240 is the percentage. We are looking for the rate. We use the formula:
[tex]r = \frac{p}{b}\\\\r = \frac{240}{400}\\\\r = \frac{3}{5}\\\\r = 0.6 = 60 percent[/tex]
n is 60.
- 2.4 is 30% of n
30% is the rate, n is the base, so 2.4 is the percentage. We are looking for the base. We use the formula:
[tex]b = \frac{p}{r} \\\\b = \frac{2.4}{0.3} \\\\b = \frac{24}{3}\\\\b = 8[/tex]
n is 8.
- 225 is 25% of n
25% is the rate, n is the base, so 225 is the percentage. We are looking for the base. We use the formula:
[tex]b = \frac{p}{r} \\\\b = \frac{225}{0.25}\\\\b = \frac{22500}{25}\\\\b = 900[/tex]
n is 900.
- 70% of n is 14.7
70% is the rate, n is the base, so 14.7 is the percentage. We are looking for the base. We use the formula:
[tex]b = \frac{p}{r} \\\\b = \frac{14.7}{0.7}\\\\b = \frac{147}{7}\\\\b = 21[/tex]
n is 21.
- 113 is 13% of n
13% is the rate, n is the base, so 113 is the percentage. We are looking for the base. We use the formula:
[tex]b = \frac{p}{r} \\\\b = \frac{113}{0.13}\\\\b = \frac{11300}{13}\\[/tex]
n is[tex]\frac{11300}{13}[/tex].
- 28% of n is 196
28% is the rate, n is the base, so 196 is the percentage. We are looking for the base. We use the formula:
[tex]b = \frac{p}{r} \\\\b = \frac{196}{0.28}\\\\b = \frac{19600}{28}\\\\b = 700[/tex]
n is 700.
- 35% of n is 120
35% is the rate, n is the base, so 1200 is the percentage. We are looking for the base. We use the formula:
[tex]b = \frac{p}{r} \\\\b = \frac{1200}{0.35} \\\\b = \frac{120000}{35}\\\\b = \frac{24000}{7}[/tex]
n is [tex]\frac{24000}{7}[/tex].
- 175.5 is 11% of n
11% is the rate, n is the base, so 175.5 is the percentage. We are looking for the base. We use the formula:
[tex]b = \frac{p}{r} \\\\b = \frac{175.5}{0.11}\\\\b = \frac{17550}{11}\\[/tex]
n is [tex]\frac{17550}{11}[/tex].
- n is 40% of 65
40% is the rate, 65 is the base, so n is the percentage. We are looking for the percentage. We use the formula:
[tex]p =br\\\\p = 0.40*65\\\\p=26[/tex]
n is 26.
To know more about the percentage, base and rate, click here:
brainly.ph/question/1857664
