If everyone had the same body proportions, your weight in pounds would vary directly with the cube of your height in feet. Assume the average height and weight of a female in your math class is 5'5" and 135 pounds. Use this information to write a variation equation then use it to find the weight of the female below if they had the same body type as the average female. Round answer to the nearest pound.
Kelly 5'4"
To write the variation equation, we need to establish the relationship between height and weight.
Let's convert the given heights to feet:
Average female height = 5'5" = 5 + 5/12 = 5.42 feet
Kelly's height = 5'4" = 5 + 4/12 = 5.33 feet
According to the problem, weight varies directly with the cube of the height. So, the variation equation can be written as:
Weight = k * (Height)^3
To find the value of k, we can use the information given for the average female:
Weight (average female) = 135 pounds
Height (average female) = 5.42 feet
Using these values in the variation equation:
135 = k * (5.42)^3
Now, let's solve for k:
k = 135 / (5.42)^3
k ≈ 0.0374
Now, we can substitute Kelly's height into the variation equation:
Weight (Kelly) = 0.0374 * (5.33)^3
Calculating this:
Weight (Kelly) ≈ 0.0374 * 151.053
Weight (Kelly) ≈ 5.651 pounds
Therefore, if Kelly had the same body type as the average female, her weight would be approximately 5.651 pounds. Rounded to the nearest pound, her weight would be 6 pounds.
To write a variation equation, we'll start by converting the height of the average female from feet and inches to just feet. Since 5 feet is equivalent to 60 inches, we can write the average height as 5.41667 feet (by dividing 65 inches by 12).
Let's represent the height in feet as 'h' and the weight in pounds as 'w'. According to the given information, the weight varies directly with the cube of the height.
So, we can write the variation equation as:
w = kh^3
We need to find the value of 'k' to use the equation for weight calculation. We'll substitute the average height (h) and weight (w) into the equation and solve for 'k'.
135 = k(5.41667)^3
135 = k(160.857)
Now divide both sides of the equation by 160.857 to solve for 'k':
k = 135 / 160.857
k ≈ 0.8399
Now that we have the value of 'k', we can use the variation equation to find the weight of Kelly, who has a height of 5'4" (which is approximately equivalent to 5.33333 feet after converting inches to feet).
Let's substitute the height of Kelly into the equation and calculate her weight:
w = 0.8399 * (5.33333)^3
w ≈ 133.89 pounds
So, if Kelly had the same body type as the average female, her weight would be approximately 134 pounds (rounded to the nearest pound).
w = k h^3 ... k = 135 / [(65 / 12)^3]
Kelly ... w = 135 [(64 / 65)^3]