Answer:
Step-by-step explanation:
Base, Rate and Percentage
The given statements above involve base, rate and percentage. Remember that the base is 100% or the whole amount, the rate is the number written with the percent symbol (%) and the percentage is the part of a whole. To know whether the given statement is true or false, you have to solve for either of them. Below are the formulas that you can use:
base = percentage ÷ rate
percentage = base × rate
rate = percentage ÷ base × 100
Solution:
1. Twenty percent of 56 is 11.2
(Solve for the percentage. Remember to convert the rate to decimal.)
percentage = base × rate
11.2 = 56 × 20%
11.2 = 56 × 0.20
11.2 = 11.2 ✔
TRUE
2. 14.5% of 90 is n. The value of n is 15.
(Solve for the percentage.)
percentage = base × rate
15 = 90 × 14.5%
15 = 90 × 0.145
15 = 13.05 ✖
The value of n should be 13.05, not 15.
FALSE
3. 25% of 275 is 68.85.
(Solve for the percentage.)
percentage = base × rate
68.85 = 275 × 25%
68.85 = 275 × 0.25
68.85 = 68.75 ✖
It should be 68.75, not 68.85.
4. n% of 670 is 302. The value of n is 46.
(Solve for the rate.)
rate = percentage ÷ base × 100
46% = 302 ÷ 670 × 100
46% = 0.4507 × 100
46% = 45.07% ✖
The rate should be 45.07%.
FALSE
5. n% of 680 is 156.4. The value of n is 23.
(Solve for the rate.)
rate = percentage ÷ base × 100
23% = 156.4 ÷ 680 × 100
23% = 0.23 × 100
23% = 23% ✔
TRUE
To study word problems involving base, rate and percentage, visit the links:
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