Gabby has a bag containing 36 nickels and quarters. The total value of the coins is $5. How many quarters does gabby have?

There are 20 nickels and 16 quarters

Solution:

Let "n" be the number of nickels

Let "q" be the number of quarters

We know that,

1 nickel = 0.05 dollar

1 quarter = 0.25 dollar

Gabby has a bag containing 36 nickels and quarters

Therefore,

n + q = 36

n = 36 - q ------- eqn 1

The total value of the coins is $5

Thus we frame a equation as:

number of nickels x 1 nickel + number of quarters x 1 quarter = 5

0.05n + 0.25q = 5 ------- eqn 2

Substitute eqn 1 in eqn 2

0.05(36 - q) + 0.25q = 5

1.8 - 0.05q + 0.25q = 5

0.2q = 3.2

q = 16

Substitute q = 16 in eqn 1

n = 36 - 16

n = 20

Thus there are 20 nickels and 16 quarters

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: