Question

Ralph opened a savings account with a deposit of $100. Every month after that, he deposited $20 more.

a. Why is the relationship described not proportional?

b. How could the situation be changed to make the situation proportional?

Answer 1

a. The relationship is not proportional because his savings account started with $100 and then he adds 20 each month.

b. To make it proportional Ralph's savings account needs to start with $0.

Answer 2

Part a) Why is the relationship described not proportional?

we know that

A relationship between two variables, x, and y, represent a direct variation or proportional if it can be expressed in the form

`(y)/(x) =k\ or\ y=kx`

In this problem

Let

x-------> number of months

y-------> amount of money in the saving account

The problem can be modeled by the following equation

`y=20x+100`

So

`20x+100\\eq kx`

In the proportional situation for the value of x equal to zero , the value of y is also equal to zero

therefore

the answer Part a) is

The relationship is not proportional because his savings account started with $
`100`

Part b) How could the situation be changed to make the situation proportional?

To make it proportional Ralph's savings account needs to start with $
`0`

so

we make the initial deposit equal to zero, maintaining the monthly deposits of $
`20`, the equation would be

`y=20x`