Question
The mathematical model StartFraction Upper W Over 2 EndFraction minus 3 Upper H equals 53
describes a weight, W, in pounds, that lies within the healthy weight range for a person whose height is H inches over 5 feet. Use the formula to find a healthy weight for a person whose height is 6'2". (Hint: Upper H equals 14 because this person's height is 14 inches over 5 feet.) How many pounds is this healthy weight above the lower end of the range shown by the bar graph?
A side-by-side bar graph titled Healthy Weight Ranges for Males and Females, Ages 19 to 34 has a horizontal axis labeled Height with the classes 5 feet 4 inches, 5 feet 6 inches, 5 feet 8 inches, 5 feet 10 inches, 6 feet 0 inches, and 6 feet 2 inches and a vertical axis labeled Weight in pounds from 0 to 240 in increments of 20. Two vertical bars are above each of the horizontal axis labels, where the left bar represents the lower end of range and the right bar represents the upper end of range. The lower and upper ends are as follows, with the height listed first and the lower and upper limits next from left to right: 5 feet 4 inches, 111 and 146; 5 feet 6 inches, 118 and 155; 5 feet 8 inches, 125 and 164; 5 feet 10 inches, 132 and 174; 6 feet 0 inches, 140 and 184; 6 feet 2 inches, 148 and 195. Each bar is labeled with its height.
Healthy Weight Ranges for Males and Females, Ages 19 to 34
5'4"
5'6"
5'8"
5'10"
6'0"
6'2"
0
40
80
120
160
200
240
Weight (pounds)
Lower end of range
Upper end of range
111
146
118
155
125
164
132
174
140
184
148
195
Height
Question content area bottom
Part 1
According to the model, a healthy weight of a person 6'2" tall is
enter your response here pounds.
describes a weight, W, in pounds, that lies within the healthy weight range for a person whose height is H inches over 5 feet. Use the formula to find a healthy weight for a person whose height is 6'2". (Hint: Upper H equals 14 because this person's height is 14 inches over 5 feet.) How many pounds is this healthy weight above the lower end of the range shown by the bar graph?
A side-by-side bar graph titled Healthy Weight Ranges for Males and Females, Ages 19 to 34 has a horizontal axis labeled Height with the classes 5 feet 4 inches, 5 feet 6 inches, 5 feet 8 inches, 5 feet 10 inches, 6 feet 0 inches, and 6 feet 2 inches and a vertical axis labeled Weight in pounds from 0 to 240 in increments of 20. Two vertical bars are above each of the horizontal axis labels, where the left bar represents the lower end of range and the right bar represents the upper end of range. The lower and upper ends are as follows, with the height listed first and the lower and upper limits next from left to right: 5 feet 4 inches, 111 and 146; 5 feet 6 inches, 118 and 155; 5 feet 8 inches, 125 and 164; 5 feet 10 inches, 132 and 174; 6 feet 0 inches, 140 and 184; 6 feet 2 inches, 148 and 195. Each bar is labeled with its height.
Healthy Weight Ranges for Males and Females, Ages 19 to 34
5'4"
5'6"
5'8"
5'10"
6'0"
6'2"
0
40
80
120
160
200
240
Weight (pounds)
Lower end of range
Upper end of range
111
146
118
155
125
164
132
174
140
184
148
195
Height
Question content area bottom
Part 1
According to the model, a healthy weight of a person 6'2" tall is
enter your response here pounds.
Answers
GPT-4o mini
To find the healthy weight \(W\) for a person who is 6'2" tall, we first need to determine the value of \(H\). Given that \(H\) is the number of inches over 5 feet, we can calculate \(H\) as follows:
A height of 6 feet equals 72 inches (since 1 foot = 12 inches). Therefore, a height of 6'2" is:
\[
72 + 2 = 74 \text{ inches}
\]
Since \(H\) is the number of inches over 5 feet:
\[
H = 74 - 60 = 14 \text{ inches}
\]
Now, we can substitute \(H = 14\) into the model:
\[
\frac{W}{2} - 3H = 53
\]
Substituting \(H\) into the equation:
\[
\frac{W}{2} - 3(14) = 53
\]
Calculating \(3(14)\):
\[
\frac{W}{2} - 42 = 53
\]
Now add 42 to both sides:
\[
\frac{W}{2} = 53 + 42
\]
\[
\frac{W}{2} = 95
\]
Now, multiply both sides by 2 to isolate \(W\):
\[
W = 190
\]
So, according to the model, a healthy weight for a person 6'2" tall is **190 pounds**.
Next, we need to determine how many pounds this healthy weight is above the lower end of the range for someone who is 6'2". From the data provided:
- The lower end of the healthy weight range for 6'2" is **148 pounds**.
Now, we will find how many pounds 190 is above this lower limit:
\[
190 - 148 = 42
\]
Thus, the healthy weight of a 6'2" tall person according to the model is **42 pounds above the lower end of the range**.
A height of 6 feet equals 72 inches (since 1 foot = 12 inches). Therefore, a height of 6'2" is:
\[
72 + 2 = 74 \text{ inches}
\]
Since \(H\) is the number of inches over 5 feet:
\[
H = 74 - 60 = 14 \text{ inches}
\]
Now, we can substitute \(H = 14\) into the model:
\[
\frac{W}{2} - 3H = 53
\]
Substituting \(H\) into the equation:
\[
\frac{W}{2} - 3(14) = 53
\]
Calculating \(3(14)\):
\[
\frac{W}{2} - 42 = 53
\]
Now add 42 to both sides:
\[
\frac{W}{2} = 53 + 42
\]
\[
\frac{W}{2} = 95
\]
Now, multiply both sides by 2 to isolate \(W\):
\[
W = 190
\]
So, according to the model, a healthy weight for a person 6'2" tall is **190 pounds**.
Next, we need to determine how many pounds this healthy weight is above the lower end of the range for someone who is 6'2". From the data provided:
- The lower end of the healthy weight range for 6'2" is **148 pounds**.
Now, we will find how many pounds 190 is above this lower limit:
\[
190 - 148 = 42
\]
Thus, the healthy weight of a 6'2" tall person according to the model is **42 pounds above the lower end of the range**.