Elina is gathering up change she has saved. She has a total of $2.60. All of her change is in either nickels, dimes, or quarters. She has twice as many dimes as quarters and two less quarters than nickels.
(a) Is it possible that Elina has eight dimes, four quarters, and six nickels? Explain.

(b) Is it possible that Elina has 12 dimes, four quarters and eight nickels? Explain.

(c) If the number of quarters Elina has is represented by the variable n, write an equation that models this
problem and solve it for the number of each type of coin.

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

step-by-step explanation:

i have done this all on a piece of paper but idk how to put it on here cuz it needs to be drawn