Question
Sunscreens block harmful ultraviolet $\text{(UV)}$ rays produced by the sun. Each sunscreen has a Sun Protection Factor $\text{(SPF)}$ that tells you how many minutes you can stay in the sun before you receive one minute of burning $\text{UV}$ rays. For example, if you apply sunscreen with $\text{SPF}\ 15$, you get $1$ minute of $\text{UV}$ rays for every $15$ minutes you stay in the sun.
$1.$ A sunscreen with $\text{SPF}$ $15$ allows only$\frac{1}{15}$ of the sun’s $\text{UV}$ rays. What per cent of $\text{UV}$ rays does the sunscreen abort?
$2.$ Suppose a sunscreen allows $25\%$ of the sun’s $\text{UV}$ rays.
$a.$ What fraction of $\text{UV}$ rays does this sunscreen block? Give your answer in lowest terms.
$b.$ Use your answer from Part $(a)$ to calculate this sunscreen’s $\text{SPF}$. Explain how you found your answer.
$3.$ A label on a sunscreen with $\text{SPF}\ 30$ claims that the sunscreen blocks about $97\%$ of harmful $\text{UV}$ rays. Assuming the $\text{SPF}$ factor is accurate, is this claim true? Explain.

Answer

$i.$ A sunscreen with $\text{SPF}\ \ 15$ allows only $\frac{1}{15}$ of the sun’s $\text{UV}$ rays
It means$=1-\frac{1}{15}=\frac{14}{15}$
In percentage$\frac{\frac{14}{15}}{1}\times100=\frac{1400}{15}=93.333\%$
$ii.$
$a.$ Sunscreen allows $25\%$ of the sun’s $\text{UV}$ rays
It blocks $\text{UV}$ rays$=100-25=75\%=\frac{75}{100}=\frac{3}{4}$
$b.$ Sunscreen allows $25\%$ on $\frac{3}{4}$ of $\text{UV}$ rays. It means, it protect$=1-\frac{3}{4}=\frac{1}{4}$ of $\text{UV}$ rays Hence, it’s a $\text{SPF}\ \ 4$.
$iii.$ False,
According to the claim, for $\frac{3}{100}$ affect of $\text{UV}$ rays
$1$ minute$=33\frac{1}{3}\text{SPF}$
Affect $\neq\ 30\ \text{SPF}$

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