Question

john is weighing his jars of coins. his jar of pennies weighs 84.96 ounces, and his jar of nickels weighs 3.11 kilograms. there are 0.0283495 kilograms per ounce. which jar weighs more, and how many more pounds does it weigh?
a. the jar of pennies weighs 8.41 pounds more than the jar of nickels.
b. the jar of pennies weighs 0.089 pounds more than the jar of nickels.
c. the jar of nickels weighs 2.06 pounds more than the jar of pennies.
d. the jar of nickels weighs 1.55 pounds more than the jar of pennies.

Explanation:

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<reasoning>

Convert penny jar weight to kilograms

Using the Unit Conversion and Dimensional Analysis knowledge points
\[
W_{\text{p, kg}} = 84.96\text{ oz} \times 0.0283495\text{ kg/oz} \approx 2.40857\text{ kg}
\]

Compare jar weights in kilograms

Using the Mass Units Comparison knowledge point
\[

$$\begin{aligned} W_{\text{n, kg}} &= 3.11\text{ kg}\\ W_{\text{p, kg}} &\approx 2.40857\text{ kg}\\ W_{\text{n, kg}} &> W_{\text{p, kg}} \end{aligned}$$

\]
The jar of nickels weighs more.

Calculate the weight difference in kilograms

Using the Mass Units Comparison knowledge point
\[
\Delta W_{\text{kg}} = 3.11\text{ kg} - 2.40857\text{ kg} \approx 0.70143\text{ kg}
\]

Convert the weight difference to pounds

Using the Unit Conversion and Dimensional Analysis knowledge points
\[

$$\begin{aligned} 1\text{ lb} &= 16\text{ oz}\\ 1\text{ lb} &= 16\text{ oz} \times 0.0283495\text{ kg/oz} \approx 0.453592\text{ kg}\\ \Delta W_{\text{lb}} &= \frac{0.70143\text{ kg}}{0.453592\text{ kg/lb}} \approx 1.5464\text{ lb} \approx 1.55\text{ lb} \end{aligned}$$

\]
The jar of nickels weighs approximately \(1.55\text{ pounds}\) more than the jar of pennies.
</reasoning>

<answer>
<mcq-option>a. The jar of pennies weighs 8.41 pounds more than the jar of nickels.</mcq-option>
<mcq-option>b. The jar of pennies weighs 0.089 pounds more than the jar of nickels.</mcq-option>
<mcq-option>c. The jar of nickels weighs 2.06 pounds more than the jar of pennies.</mcq-option>
<mcq-correct>d. The jar of nickels weighs 1.55 pounds more than the jar of pennies.</mcq-correct>
</answer>

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Answer:

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<reasoning>

Convert penny jar weight to kilograms

Using the Unit Conversion and Dimensional Analysis knowledge points
\[
W_{\text{p, kg}} = 84.96\text{ oz} \times 0.0283495\text{ kg/oz} \approx 2.40857\text{ kg}
\]

Compare jar weights in kilograms

Using the Mass Units Comparison knowledge point
\[

$$\begin{aligned} W_{\text{n, kg}} &= 3.11\text{ kg}\\ W_{\text{p, kg}} &\approx 2.40857\text{ kg}\\ W_{\text{n, kg}} &> W_{\text{p, kg}} \end{aligned}$$

\]
The jar of nickels weighs more.

Calculate the weight difference in kilograms

Using the Mass Units Comparison knowledge point
\[
\Delta W_{\text{kg}} = 3.11\text{ kg} - 2.40857\text{ kg} \approx 0.70143\text{ kg}
\]

Convert the weight difference to pounds

Using the Unit Conversion and Dimensional Analysis knowledge points
\[

$$\begin{aligned} 1\text{ lb} &= 16\text{ oz}\\ 1\text{ lb} &= 16\text{ oz} \times 0.0283495\text{ kg/oz} \approx 0.453592\text{ kg}\\ \Delta W_{\text{lb}} &= \frac{0.70143\text{ kg}}{0.453592\text{ kg/lb}} \approx 1.5464\text{ lb} \approx 1.55\text{ lb} \end{aligned}$$

\]
The jar of nickels weighs approximately \(1.55\text{ pounds}\) more than the jar of pennies.
</reasoning>

<answer>
<mcq-option>a. The jar of pennies weighs 8.41 pounds more than the jar of nickels.</mcq-option>
<mcq-option>b. The jar of pennies weighs 0.089 pounds more than the jar of nickels.</mcq-option>
<mcq-option>c. The jar of nickels weighs 2.06 pounds more than the jar of pennies.</mcq-option>
<mcq-correct>d. The jar of nickels weighs 1.55 pounds more than the jar of pennies.</mcq-correct>
</answer>

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