# A golf ball weighs about 45.9 grams. About how many ounces would a dozen golf balls weigh?

Dec 12, 2016

I've set up a conversion equation:

You can just say it out loud what you're trying to do and that will help you write out your ratios.

45.9 grams per 1 ball
1 ounce per 28.35 grams
We have 12 balls

$\frac{45.9 g}{b a l l} \cdot \frac{1 o z}{28.35 g} \cdot 12 \left(b a l l\right)$

$\frac{45.9 \cancel{g}}{\cancel{b a l l}} \cdot \frac{1 o z}{28.35 \cancel{g}} \cdot 12 \left(\cancel{b a l l}\right)$

$= \frac{45.9 \cdot 12}{28.35} \approx 19.4 o z$

Dec 13, 2016

so the weight of 12 balls is 19.43 ounces rounded to 2 decimal places

#### Explanation:

Using Matt B's conversion

1 ounce per 28.35 grams
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Determine the weight of 12 balls in grams}}$

Given:$\text{ }$1 ball weighs 45.9 grams

Expressing this as a ratio for 12 balls:

$\left(\text{ball count")/("total weight") = 1/(45.9" grams}\right)$

So for 12 balls we have (12xx1" balls")/(12xx45.9" grams") = (12" balls")/(color(red)(550.8" grams"))
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$\textcolor{b l u e}{\text{Converting the grams to ounces}}$

If 1 ounce is the same weight as 28.35 grams then again by using ratio:

$\left(\text{ounces")/("grams}\right) \to \frac{1}{28.35} \equiv \frac{1 \div 28.35}{28.35 \div 28.35} = \frac{\textcolor{g r e e n}{1 \div 28.35}}{1}$

I have not completed the division on the top yet as this will introduce rounding errors.

So $\textcolor{g r e e n}{\text{each gram is worth "1-:28.35=" ounces}}$, but we have $\textcolor{red}{550.8 \text{ grams}}$

So " " (12" balls")/(color(red)(550.8" grams")) =(12"balls")/(color(red)(550.8)color(green)(xx1-:28.35))

$= \text{ "(12" balls")/(19.4285..."ounces}$

so the weight of 12 balls is 19.43 ounces rounded to 2 decimal places