Question

5 from unit 2, lesson 3
one kilogram is 2.2 pounds. complete the tables. what is the interpretation of the constant of proportionality in each case?

kilograms	pounds
7
30
0.5

____ pounds per kilogram

pounds	kilograms
11
5.5
1

____ kilogram per pound

Explanation:

Step1: Fill left table (kilograms to pounds)

To convert kilograms to pounds, use the conversion factor \( 2.2 \) pounds per kilogram. So, for \( k \) kilograms, pounds \( = 2.2 \times k \).

• For \( 7 \) kilograms: \( 2.2 \times 7 = 15.4 \)
• For \( 30 \) kilograms: \( 2.2 \times 30 = 66 \)
• For \( 0.5 \) kilograms: \( 2.2 \times 0.5 = 1.1 \)

Step2: Fill right table (pounds to kilograms)

To convert pounds to kilograms, use the conversion factor \( \frac{1}{2.2} \) kilograms per pound (since \( 2.2 \) pounds = \( 1 \) kilogram). So, for \( p \) pounds, kilograms \( = \frac{p}{2.2} \).

• For \( 11 \) pounds: \( \frac{11}{2.2} = 5 \)
• For \( 5.5 \) pounds: \( \frac{5.5}{2.2} = 2.5 \)
• For \( 1 \) pound: \( \frac{1}{2.2} = \frac{5}{11} \approx 0.4545 \) (or keep as \( \frac{1}{2.2} \))

Step3: Determine constants of proportionality

• Left table (pounds per kilogram): The conversion factor is \( 2.2 \), as \( 1 \) kilogram \( = 2.2 \) pounds.
• Right table (kilograms per pound): The conversion factor is \( \frac{1}{2.2} = \frac{5}{11} \approx 0.4545 \) (or \( \frac{1}{2.2} \) simplifies to \( \frac{5}{11} \)).

Answer:

Left table (kilograms to pounds) filled values: \( 7 \) kg → \( 15.4 \) lb, \( 30 \) kg → \( 66 \) lb, \( 0.5 \) kg → \( 1.1 \) lb.
Right table (pounds to kilograms) filled values: \( 11 \) lb → \( 5 \) kg, \( 5.5 \) lb → \( 2.5 \) kg, \( 1 \) lb → \( \frac{5}{11} \) (or \( \approx 0.45 \)) kg.
Constant of proportionality (left): \( 2.2 \) pounds per kilogram.
Constant of proportionality (right): \( \frac{5}{11} \) (or \( \approx 0.45 \)) kilograms per pound.

(For the blanks at the bottom:
Left blank: \( \boldsymbol{2.2} \)
Right blank: \( \boldsymbol{\frac{5}{11}} \) (or \( \approx 0.45 \)) )