Question

match each individual to the correct category using height and weight information. amir is five feet nine inches tall and weighs 120 pounds. julie is five feet seven inches tall and weighs 170 pounds. pat is five feet tall and weighs 100 pounds.

Explanation:

To solve this, we can use the Body Mass Index (BMI) concept. BMI is calculated as weight (in pounds) divided by height (in inches) squared, multiplied by 703. The formula is \( BMI=\frac{weight(lb)\times703}{height(in)^2} \).

Step 1: Calculate BMI for Amir

Amir's height: 5 feet 9 inches = \( 5\times12 + 9 = 69 \) inches. Weight = 120 lb.
\( BMI=\frac{120\times703}{69^2}=\frac{84360}{4761}\approx17.72 \)
BMI below 18.5 is underweight? Wait, no, 17.72 is underweight? Wait, no, wait: Wait, underweight is BMI < 18.5, normal is 18.5 - 24.9, overweight is 25 - 29.9, obese is 30+. Wait, Amir's BMI is ~17.72 (underweight? Wait, no, maybe I miscalculated. Wait 5ft9in is 69 inches. 120 pounds. Let's recalculate: \( 120 / (69/39.37)^2 \)? No, the standard BMI formula in pounds and inches is \( BMI = (weight / height^2) \times 703 \). So \( 120 / (69^2) \times 703 = (120 \times 703) / 4761 = 84360 / 4761 ≈ 17.72 \). So underweight is BMI < 18.5, so Amir is underweight? Wait, no, maybe the categories here are simplified. Wait, let's check Pat: 5ft is 60 inches, weight 100 lb. \( BMI = (100 \times 703)/(60^2) = 70300 / 3600 ≈ 19.53 \), which is normal (18.5 - 24.9). Julie: 5ft7in = 67 inches, weight 170 lb. \( BMI=(170\times703)/(67^2)=119510 / 4489≈26.62 \), which is overweight (25 - 29.9). Wait, but the initial matching:

Wait the problem has:

Underweight, Overweight, Normal on the left.

Amir: 5'9" (69in), 120lb. Let's see typical weight ranges. For 5'9" (69in), the healthy weight range (BMI 18.5 - 24.9) is weight between \( 18.5\times(69)^2 /703 \) and \( 24.9\times(69)^2 /703 \). Calculate lower bound: \( 18.5\times4761 /703 ≈ (18.5\times4761)/703 ≈ 88078.5 /703 ≈ 125.3 \) lb. Upper bound: \( 24.9\times4761 /703 ≈ 118548.9 /703 ≈ 168.6 \) lb. So Amir weighs 120 lb, which is below 125.3, so underweight? Wait no, 120 is less than 125, so underweight? Wait but maybe the categories are simplified. Wait Pat: 5ft (60in), weight 100lb. For 5ft, healthy weight (BMI 18.5 -24.9) is \( 18.5\times60^2 /703 ≈ 18.5\times3600 /703 ≈ 66600 /703 ≈ 94.7 \) to \( 24.9\times3600 /703 ≈ 89640 /703 ≈ 127.5 \) lb. Pat is 100lb, which is between 94.7 and 127.5, so normal. Julie: 5'7" (67in), weight 170lb. For 5'7", healthy weight is \( 18.5\times67^2 /703 ≈ 18.5\times4489 /703 ≈ 83046.5 /703 ≈ 118.1 \) to \( 24.9\times4489 /703 ≈ 111776.1 /703 ≈ 159.0 \) lb. Julie is 170lb, which is above 159, so overweight.

So:

Amir: Underweight (since 120 < 125.3)

Pat: Normal (100 is between 94.7 and 127.5)

Julie: Overweight (170 > 159)

Wait but the initial matching in the problem:

The left has Underweight, Overweight, Normal.

The right has Amir, Pat, Julie with?

So the correct matches are:

Underweight - Amir

Normal - Pat

Overweight - Julie

Wait let's recheck:

Amir: 5'9" (69in), 120lb. BMI ~17.7 (underweight, since <18.5)

Pat: 5' (60in), 100lb. BMI ~19.5 (normal, 18.5-24.9)

Julie: 5'7" (67in), 170lb. BMI ~26.6 (overweight, 25-29.9)

So the matches are:

Underweight: Amir

Normal: Pat

Overweight: Julie

So the correct pairing is:

Underweight - Amir

Normal - Pat

Overweight - Julie

Answer:

To solve this, we can use the Body Mass Index (BMI) concept. BMI is calculated as weight (in pounds) divided by height (in inches) squared, multiplied by 703. The formula is \( BMI=\frac{weight(lb)\times703}{height(in)^2} \).

Step 1: Calculate BMI for Amir

Amir's height: 5 feet 9 inches = \( 5\times12 + 9 = 69 \) inches. Weight = 120 lb.
\( BMI=\frac{120\times703}{69^2}=\frac{84360}{4761}\approx17.72 \)
BMI below 18.5 is underweight? Wait, no, 17.72 is underweight? Wait, no, wait: Wait, underweight is BMI < 18.5, normal is 18.5 - 24.9, overweight is 25 - 29.9, obese is 30+. Wait, Amir's BMI is ~17.72 (underweight? Wait, no, maybe I miscalculated. Wait 5ft9in is 69 inches. 120 pounds. Let's recalculate: \( 120 / (69/39.37)^2 \)? No, the standard BMI formula in pounds and inches is \( BMI = (weight / height^2) \times 703 \). So \( 120 / (69^2) \times 703 = (120 \times 703) / 4761 = 84360 / 4761 ≈ 17.72 \). So underweight is BMI < 18.5, so Amir is underweight? Wait, no, maybe the categories here are simplified. Wait, let's check Pat: 5ft is 60 inches, weight 100 lb. \( BMI = (100 \times 703)/(60^2) = 70300 / 3600 ≈ 19.53 \), which is normal (18.5 - 24.9). Julie: 5ft7in = 67 inches, weight 170 lb. \( BMI=(170\times703)/(67^2)=119510 / 4489≈26.62 \), which is overweight (25 - 29.9). Wait, but the initial matching:

Wait the problem has:

Underweight, Overweight, Normal on the left.

Amir: 5'9" (69in), 120lb. Let's see typical weight ranges. For 5'9" (69in), the healthy weight range (BMI 18.5 - 24.9) is weight between \( 18.5\times(69)^2 /703 \) and \( 24.9\times(69)^2 /703 \). Calculate lower bound: \( 18.5\times4761 /703 ≈ (18.5\times4761)/703 ≈ 88078.5 /703 ≈ 125.3 \) lb. Upper bound: \( 24.9\times4761 /703 ≈ 118548.9 /703 ≈ 168.6 \) lb. So Amir weighs 120 lb, which is below 125.3, so underweight? Wait no, 120 is less than 125, so underweight? Wait but maybe the categories are simplified. Wait Pat: 5ft (60in), weight 100lb. For 5ft, healthy weight (BMI 18.5 -24.9) is \( 18.5\times60^2 /703 ≈ 18.5\times3600 /703 ≈ 66600 /703 ≈ 94.7 \) to \( 24.9\times3600 /703 ≈ 89640 /703 ≈ 127.5 \) lb. Pat is 100lb, which is between 94.7 and 127.5, so normal. Julie: 5'7" (67in), weight 170lb. For 5'7", healthy weight is \( 18.5\times67^2 /703 ≈ 18.5\times4489 /703 ≈ 83046.5 /703 ≈ 118.1 \) to \( 24.9\times4489 /703 ≈ 111776.1 /703 ≈ 159.0 \) lb. Julie is 170lb, which is above 159, so overweight.

So:

Amir: Underweight (since 120 < 125.3)

Pat: Normal (100 is between 94.7 and 127.5)

Julie: Overweight (170 > 159)

Wait but the initial matching in the problem:

The left has Underweight, Overweight, Normal.

The right has Amir, Pat, Julie with?

So the correct matches are:

Underweight - Amir

Normal - Pat

Overweight - Julie

Wait let's recheck:

Amir: 5'9" (69in), 120lb. BMI ~17.7 (underweight, since <18.5)

Pat: 5' (60in), 100lb. BMI ~19.5 (normal, 18.5-24.9)

Julie: 5'7" (67in), 170lb. BMI ~26.6 (overweight, 25-29.9)

So the matches are:

Underweight: Amir

Normal: Pat

Overweight: Julie

So the correct pairing is:

Underweight - Amir

Normal - Pat

Overweight - Julie