Word Problem - Parts of fraction.

Question

I am having difficulty with this problem , am I doing something wrong here ?

To mail an airmail a letter costs $60$ cents for the first half ounce and $15$ cents for each additional ounce or fraction thereof.What would be the cost of mailing a letter that weighs $2.1$ ounces.

Here is how I am doing it:

$$\frac{2.1}{0.5}=4.2 \text{ parts}.$$

Since the First part costs $60$ cents so $4.2-1 = 3.2$. This means

$$1 + 3.2 = 60 \text{ cents} + 3.2(15 \text{ cents}) = 60 \text{ cents} + 48 \text{ cents} = 1.08 \text{ dollars}.$$

However the answer is supposed to be $1.20$. Any suggestions on what I am doing wrong?

Answer 1

The critical phrase is "for each additional ounce or fraction thereof". The first half ounce costs 60 cents, then you have 1.6 ounces left. This is one ounce and some more, so you should pay 2(15 cents) for them, making a total of 90 cents. Knowing how US postage rates are usually quoted, your book probably meant to say 15 cents per additional half ounce or fraction, in which case you would have 3.2 additional half ounces, which rounds up to 4, and the total would be 60 cents+4(15 cents)=1.20.

Answer 2

You are computing wrong, because while the first half ounce costs 60 cents, after that you get charged for each full ounce.

If $w$ is the weight of the letter in ounces, the description given says that the charge for mailing the letter will be: $$\text{charge} = \left\{\begin{array}{ll} \$0.60 &\text{if }0\leq w\leq 0.5\text{ oz.}\\ \$0.75 &\text{if }0.5\lt w \leq 1.5\text{ oz.}\\ \$0.90 &\text{if }1.5\lt w\leq 2.5\text{ oz.}\\ \$1.05 &\text{if }2.5\lt w\leq 3.5\text{ oz.}\\ \$1.20 &\text{if }3.5\lt w\leq 4.5\text{ oz.}\\ \$1.35 &\text{if }4.5\lt w\leq 5.5\text{ oz.}\\ \$1.50 &\text{if }5.5\lt w\leq 6.5\text{ oz.}\\ &\vdots \end{array}\right.$$ You can see that a $2.1$ oz. letter would cost 90 cents. If the letter weighed between 3.5 and 4.5, then the cost would be \$1.20.

Now, if the additional charge was supposed to be "for each additional half ounce or fraction thereof", then the increments above would be by half ounces after the first line, instead of by full ounces, so an answer of \$1.20 would be correct.