Question

Match the real-world problem to its constant of proportionality.

Answer 1

Real word problem ⇒ constant of proportionality

$4.16 for 4 pounds of bananas ⇒ 1.04

$16.48 for 8 pounds of potatoes  ⇒ 2.06

$18.36 for 2 pizzas  ⇒ 9.18

2 cups of flour to make 36 cookies ⇒ 18

Solution:

A proportional relationship is one in which two quantities vary directly with each other.

We say the variable y varies directly as x,

if for x ∝ y

then,  x = y k

Where "k" is called constant of proportionality

$k = \frac{x}{y}$

$4.16 for 4 pounds of bananas

x = 4.16 and y = 4

$k = \frac{4.16}{4} = 1.04$

Thus constant of proportionality is 1.04

$16.48 for 8 pounds of potatoes

x = 16.48 and y = 8

$k = \frac{16.48}{8} = 2.06$

Thus constant of proportionality is 2.06

$18.36 for 2 pizzas

x = 18.36 and y = 2

$k = \frac{18.36}{2} = 9.18$

Thus constant of proportionality is 9.18

2 cups of flour to make 36 cookies

x = 36 and y = 2

$k = \frac{36}{2} = 18$

Thus constant of proportionality is 18