the body mass index ,I,can be used to determine an individuals risk for heart disease. An index less then 25 indicates a low risk. The body mass index is given by the formula,or model,I=700w/h2, where w = weight,in pounds,and H=height,in inches.Jerome is 72 inches tall.What weight will keep his body mass index between 24 an 33?
Jerome body mass index will fall between 24 and 33 for the set of all weight such that_____________< W<_____
The body mass index , I , can be used to determine an individual's risk for heart disease . An index less than 25 indicates a low risk . The body mass index is given by the 700W formula , or model , I = where W = weight , in pounds , and height , in inches Jerome is 75 inches tall . What weights will keep his body mass index between 21 H2 and 29 ? < W < Jerome's body mass index will fall between 21 and 29 for the set of all weights such that
Start with the given equation of
I=700w/h^2
I=700w/72^2 Plug in Jerome's height
I=700w/5184
Since we want the BMI to be between 24 and 33, we have to construct an inequality.
24=<700/5184=<33
Multiply all sides by 5184
5184*24=<700w*5184/5184=<33*5184
Once you delete unnecessary duplications you have the inequeality of
124416/700=<700w=<171072/700
Now all you have to do is divide by 700 on both sides as above and you will have your answer. Just remember to write it as an inequality.
Double check the math.
To find the weight range that will keep Jerome's body mass index (BMI) between 24 and 33, we need to substitute the given values into the BMI formula and solve for the weight, W.
The formula is:
I = 700W/H^2
Given:
H = 72 inches
BMI range: 24 ≤ I ≤ 33
Substituting the values into the formula, we get:
24 ≤ 700W/72^2 ≤ 33
To simplify, let's first evaluate 72^2:
72^2 = 5184
Now we can rewrite the inequality:
24 ≤ 700W/5184 ≤ 33
To isolate W, we can multiply the entire inequality by 5184:
24 * 5184 ≤ 700W ≤ 33 * 5184
So we have:
124416 ≤ 700W ≤ 171072
Divide the entire inequality by 700 to solve for W:
124416 / 700 ≤ W ≤ 171072 / 700
177.74 ≤ W ≤ 244.39
Therefore, Jerome's body mass index will fall between 24 and 33 for any weight in the range 177.74 pounds ≤ w ≤ 244.39 pounds.
To find the weight that will keep Jerome's body mass index (BMI) between 24 and 33, we can use the given formula for BMI: I = 700w/h^2, where w is the weight in pounds and h is the height in inches.
Since Jerome's height is given as 72 inches, we can substitute h = 72 into the formula to get:
I = 700w/72^2
Now we need to find the weight range that corresponds to a BMI between 24 and 33. Using the formula, we can set up the following inequalities:
24 ≤ 700w/72^2 ≤ 33
To solve these inequalities, we can start by multiplying the entire inequality by 72^2 to eliminate the denominator:
24 * 72^2 ≤ 700w ≤ 33 * 72^2
Simplifying, we have:
24 * 72^2 ≤ 700w ≤ 33 * 72^2
51840 ≤ 700w ≤ 68040
Next, divide each term by 700 to isolate w:
(51840/700) ≤ (700w/700) ≤ (68040/700)
74.057 ≤ w ≤ 97.2
Therefore, Jerome's body mass index will fall between 24 and 33 for any weight in the range of 74.057 pounds to 97.2 pounds.