Question

it takes Maya 30 minutes to solve 5 logic puzzles, and it takes Amy 28 minutes to solve 4 logic puzzles. use models to show the rate at which eachstudent solves the puzzles, in minutes per puzzles

Answer 1

Maya --->
`6\ minutes/puzzle`

Amy ---->
`7\ minutes/puzzle`

see the procedure

Explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
`k=(y)/(x)` or
`y=kx`

Let

m ---> the number of minutes

p ---> the number of puzzles

In this problem, the relationship between the variables m and p represent a proportional variation

so

`m=kp`

Maya

it takes Maya 30 minutes to solve 5 logic puzzles

we have

m=30, p=5

Determine the value of the constant of proportionality k

`k=(m)/(p)`

substitute the given values

`k=(30)/(5)=6\ minutes/puzzle`

The value of the constant k is the same that the slope or unit rate

The equation is equal to

`m=6p`

Amy

it takes Maya 28 minutes to solve 4 logic puzzles

we have

m=28, p=4

Determine the value of the constant of proportionality k

`k=(m)/(p)`

substitute the given values

`k=(28)/(4)=7\ minutes/puzzle`

The value of the constant k is the same that the slope or unit rate

The equation is equal to

`m=7p`