Question

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

$4.16 for 4 pounds of bananas
$16.48 for 8 pounds of potatoes
$18.36 for 2 pizzas
2 cups of flour to make 36 cookies

9.18,1.04,18,2.06

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 = (x)/(y)`

$4.16 for 4 pounds of bananas

x = 4.16 and y = 4

`k = (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 = (16.48)/(8) = 2.06`

Thus constant of proportionality is 2.06

$18.36 for 2 pizzas

x = 18.36 and y = 2

`k = (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 = (36)/(2) = 18`

Thus constant of proportionality is 18