SOLUTION: Greg started with a certain number of quarters. He then decided on a number of quarters he would save each day. He added the quarters he saved to the amount with which he started.

Question 1141390: Greg started with a certain number of quarters. He then decided on a number of quarters he would save each day. He added the quarters he saved to the amount with which he started.
At the end of day 2, Greg had a total of 26 quarters saved.
At the end of day 5, he had a total of 35 quarters saved.
At the end of day 8, he had a total of 44 quarters saved.
Hint: Create an x/y or t-chart and fill in the numbers with x-value representing the # of days and the y-value representing "total coins."
A. How many quarters does Greg start with (day zero)? Show or explain your work.
B. Write an equation in slope-intercept form to model the total quarters Greg has saved after x days.
C. Using the rate at which Greg is saving, explain why he can never have exactly 100 quarters saved by the end of any given day.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

He is adding 9 quarters every 3 days, or 3 quarters every day.

A. At the end of day 2, he had added 2*3=6 quarters to the starting number. Since he had 26 quarters at the end of day 2, he started with 26-6=20 quarters.

B. 20, plus 3 more for each day: literally, y = 20+3x. In slope-intercept form, y = 3x+20.

C. The starting number of 20 is 2 more than a multiple of 3. Since he adds 3 quarters each day, the total at the end of every day will be 2 more than a multiple of 3. 100 is 1 more than a multiple of 3, so he will never have 100 quarters at the end of any day.

Note that instead of explaining part C in words, you could just show that the equation 3x+20=100 has a non-integer solution.
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