Fhas 10 more marbles than i. both boys have 15 marbles combined. how many marbles does each boy have? show your work.

F has 10 marbles and I has 5 marbles.

Solution:

From question, given that F has 10 more marbles than I. Both F and I have 15 marbles together.

So the total number of marbles is 15. We can write equation as  

Total number of marbles = number of marbles of F + number of marbles of I

15 = number of marbles of F + number of marbles of I

Given in question that F has 10 more marbles that I, hence it’s clear from above equation that  number of marbles of F is 10 and number of marbles of I is 5 . so together they contain 15 marbles.  

hence F has 10 marbles and I has 5 marbles.

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}