Sally has a mass of 70 kilograms and Dave weighs 170 pounds. What is Sally’s weight as a percentage of Dave’s weight? (Round to the nearest whole percentage point and do not include units in your answer.)
Note: There are 2.205 pounds per kilogram.
The correct answer and explanation is :
To determine Sally’s weight as a percentage of Dave’s weight, we first need to convert Sally’s mass from kilograms to pounds and then calculate the percentage.
Step 1: Convert Sally’s Mass from Kilograms to Pounds
We are given that Sally has a mass of 70 kilograms, and we know that there are 2.205 pounds per kilogram. To convert Sally’s weight from kilograms to pounds, we multiply her mass by this conversion factor:
[
\text{Sally’s weight in pounds} = 70 \, \text{kg} \times 2.205 \, \text{pounds/kg} = 154.35 \, \text{pounds}
]
So, Sally weighs approximately 154.35 pounds.
Step 2: Calculate Sally’s Weight as a Percentage of Dave’s Weight
We are also told that Dave weighs 170 pounds. To find out what percentage Sally’s weight is of Dave’s weight, we use the formula for percentage:
[
\text{Percentage} = \left( \frac{\text{Sally’s weight}}{\text{Dave’s weight}} \right) \times 100
]
Substituting the values we know:
[
\text{Percentage} = \left( \frac{154.35 \, \text{pounds}}{170 \, \text{pounds}} \right) \times 100 = 0.906 \times 100 = 90.6\%
]
Step 3: Round the Result
Since the problem asks for the answer to be rounded to the nearest whole percentage point, we round 90.6% to 91%.
Final Answer:
Sally’s weight is 91% of Dave’s weight.
Explanation:
This problem involves basic unit conversion and percentage calculation. We first converted Sally’s mass in kilograms to weight in pounds using the conversion factor (2.205 pounds per kilogram). After obtaining Sally’s weight in pounds, we compared it to Dave’s weight in pounds using a percentage formula. This allowed us to determine the relative weight of Sally compared to Dave. Finally, the result was rounded to the nearest whole number as per the problem’s instructions.