The following rates are:
a) 6.67
b) 500
c) 40
d) 7.5
When two quantities of different units are compared and expressed as a ratio then it is called rate.
Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as a denominator and represented by "%".
Calculating percentage means to find the share of whole, in terms of 100. By changing the denominator of the fraction to 100.
a) Let the rate be x.
Then,
x% of 75 = 5.
[tex]\implies \frac{x}{100} (75) = 5\\\implies x = \frac{5(100)}{(75)}[/tex]
[tex]\implies x = 6.67[/tex]
b) Let the rate be y.
Then,
y% of 28 = 140
[tex]\implies \frac{y}{100} (28) = 140[/tex]
[tex]\implies \frac{y }{100} = \frac{140}{28} \\\implies \frac{y}{100} = 5\\\implies y = 500[/tex]
c) Let the rate be z.
Then,
z% of 100 = 40
[tex]\implies \frac{z}{100} (100)=40\\\implies z = 40[/tex]
d) Let the rate be w.
Then,
w% of 200 = 15
[tex]\implies \frac{w}{100} (200)= 15[/tex]
[tex]\implies w(2) = 15\\\implies w = \frac{15}{2} \\\implies w = 7.5[/tex]
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