Question

Susan started with a certain number of dollars. She then decided on a number of dollars she would save each day. She added the dollars she saved to the amount with which she started. At the end of day 2, Susan had a total of 20 dollars saved. At the end of day 5, she had a total of 32 dollars saved.

How many dollars does Susan start with? Show or explain your work.
Write an equation to model the number of dollars Susan has saved, y, after x days.

Answer 1

Susan start with 12 dollars

Equation to model the number of dollars Susan has saved, y, after x days :
`4x-y+12=0`

Explanation:

Given : She added the dollars she saved to the amount with which she started. At the end of day 2, Susan had a total of 20 dollars saved. At the end of day 5, she had a total of 32 dollars saved.

To Find: How many dollars does Susan start with? Show or explain your work. Write an equation to model the number of dollars Susan has saved, y, after x days.

Solution :

Since At the end of day 2, Susan had a total of 20 dollars saved.

⇒
`(x_(1) ,y_(1))=(2,20)`

At the end of day 5, she had a total of 32 dollars saved.

⇒
`(x_(2) ,y_(2))=(5,32)`

So, using two point slope from find the equation of line

x denotes days

y denotes dollars she saved

`y-y_(1) =(y_(2) - y_(1))/(x_(2)- x_(1))*(x-x_(1))`

`y-20 =(32-20)/(5-2)*(x-2)`

`y-20 =(12)/(3)*(x-2)`

`y-20 =4(x-2)`

`y-20 =4x-8`

`4x-y+12=0` --a

Thus the equation to model the number of dollars Susan has saved, y, after x days :
`4x-y+12=0`

Now to calculate How many dollars does Susan start with?

Put x = 0 in equation a

`4*0-y+12=0`

`y=12`

So,Susan start with 12 dollars