Question

I have always enjoyed eating tuna fish. Unfortunately, a study of the mercury content of canned tuna in 2010 found that chunk white tuna contains 0.6ppmHgand chunk light tuna contains $\mathbf{0}\mathbf{.}\mathbf{14}\mathbf{ppm}{\mathbf{.}}^{\mathbf{2}}$ The U.S. Environmental Protection Agency recommends no more than $\mathbf{0}\mathbf{.}\mathbf{1}\mathbf{\mu gHg}\mathbf{/}\mathbf{kg}$body weight per day. I weigh 68 kgHow often may I eat a can containing 6 ouncesrole="math" localid="1663301809153" $\left(1\mathrm{lb}=16\mathrm{oz}\right)$of chunk white tuna so that I do not average more than $\mathbf{0}\mathbf{.}\mathbf{1}\mathbf{\mu gHg}\mathbf{/}\mathbf{kg}$body weight per day? If I switch to chunk light tuna, how often can I eat one can?

Short answer

White tuna$=0.0665$times per day

Light tuna $=0.2853$times per day

Step-by-step solution

Definition of White tuna and Light tuna

Chunk White Albacore Tuna has smaller chunks with a mild flavor, a firm texture, and a white color, whereas Solid White Albacore Tuna has larger chunks. Chunk Light Tuna is made lastly from little tuna fish.

Converting the 0.1 ppb to ppm

According to 2010 research on mercury content in canned tuna, chunk white tuna contains 0.66ppm of mercury, while white chunk light tuna contains 0.144ppm.

The Environmental Protection Agency of the United States normally advises no more than

(1) To begin, convert the 0.1 ppb to ppm as follows:

Please note: 1 ppb $=0.001\mathrm{ppm}\left(0.1\right)\left(0.001\right)=0.0001\mathrm{ppm}\left(\mathrm{ormg}/\mathrm{kg}\right)$

Calculating the Amount of food each day

(2) If you weigh 08 kg you can consume the following amount of food each day:

$\left(68\mathrm{kg}\right)\left(0.001\mathrm{mg}/\mathrm{kg}\right)=0.0068\mathrm{mgHg}/\mathrm{day}$

Converting oz to mg OOz

(3) Next, if you eat a can of chunk tuna, convert oz to mg OOz as follows:

$6\mathrm{Oz}\times \frac{1\mathrm{lb}}{16\mathrm{oz}}=0.375\mathrm{lb}$

Please not it: $1\mathrm{lb}=0.454\mathrm{kg}$, as a result: role="math" localid="1663302440997" $3.75\mathrm{lb}\times 0.454\frac{\mathrm{kg}}{\mathrm{lb}}=0.17025\mathrm{kg}$of Tuna

Solving the mg Hg of canned tuna

(4) Then, as shown below, solve for the mg Hg of canned tuna:

$$\begin{gathered} 0.17025\mathrm{kgTuna}\times 0.6\frac{\mathrm{mgHg}}{\mathrm{kg}}=0.1022\mathrm{mgHg} \\ \mathbf{0}\mathbf{.}\mathbf{17025}\mathrm{kgTuna}\times \mathbf{0}\mathbf{.}\mathbf{14}\frac{\mathrm{mgHg}}{\mathrm{kg}}=\mathbf{0}\mathbf{.}\mathbf{023835}\mathrm{mgHg} \end{gathered}$$

Result of White tuna and Light tuna

(5) Finally, to test how much tuna you can eat in a day, do the following:

White tuna $=\frac{0.0068\mathrm{mgHg}/\mathrm{day}}{0.1022\mathrm{mgHg}}=0.0665$times per day

Light tuna $=\frac{0.0068\mathrm{mgHg}/\mathrm{day}}{0.023835\mathrm{mgHg}}=0.2853$times per day.