Tara and Ashley spent the same amount at the grocery store. Tara bought 5 pounds of apples. Ashley bought 3 pounds of apples and $5 worth other groceries. How much does one pound of apples cost?

one pound of apple cost $2.5

Step-by-step explanation:

Let the amount they both spent at the grocery store be y and x be the price of apples per pound.

Since Tara bought 5 pounds of apples, 5x = y (1) and Ashley bought 3 pounds of apples and $5 worth other groceries, 3x + 5 = y (2).

Equating both expressions, 5x = 3x + 5

collecting like terms,

5x - 3x = 5

2x = 5

dividing both sides by 2, we have

x = 5/2

x = 2.5

So one pound of apple cost $2.5

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}