Question

There are 6 quarters in a jar .jill adds 2 quarters everyday which linear equation represents the total amount of quarters in the jar after x days

Answer 1

Let y be the total number of quarters in the jar after day x. How many quarters does Jill have on day 0? Clearly 6, since that information was stated in the question. So, we know that each additional day is going to be adding to that initial six. One day 1, when x=1, we have 2 more quarters, or:

y = 6 + 2 = 8 quarters altogether.

When x = 2, we have:

y = 6 + 2 + 2 = 10 quarters altogether.

And when x = 3, we have:

y = 6 + 2 + 2 + 2 = 12 quarters altogether.

Do you notice a pattern here? What's the relationship between the number of 2's and the value of x? How can you use that relationship to come up with a general equation?

Answer 2

The initial number of quarters in a jar is 6. We know that Jill adds 2 quarters everyday, and by hypothesis, x represents the number of days.
So after x days, Jill has added 2x quarters.
Which means that after x days, the total numbers of quarters in the jar is:
2x + 6.

So the linear equation that represents the total amount of quarters in the jar after x days is: f(x) = 2x + 6

Hope this helps! :)