There are 1001 pennies lined up on a table. I come along and replace every 2nd coin with a Nickle. Then, replace every 3rd coin with a Dime. Finally, I replace every 4th coin with a Quarter. How much money is on the table?

$99.19

Step-by-step explanation:

Problem:

On a table there are 1001 pennies lined up in a row. I come along and replace every second coin with a nickel.  Then I replace every third coin with a dime.  Finally, I replace every fourth coin with a quarter.  How much money is on the table now? Why is twelve important?

Solution:

Our first step was to make a line of pennies (as long as possible) in order to see if we could figure out a pattern that would help us determine the total amount of money on the table.  

Then we went through and replace every second coin with a nickel.

Then we went through and replaced every third coin with a dime.

Then we went through and replaced every fourth coin with a quarter.

As a group we then tried to decipher if there was a pattern that would help us determine the total value of coins.  We then noticed that there was a pattern of twelve coins.

= $1.19

= $1.19

= $1.19

We determined the number of times the pattern of twelve coins repeated in the 1001 coins:

1001 ÷ 12 = 83 R5

Since we knew that the pattern repeated itself 83 full times and each time the dollar value is $1.19 we counted to determine the cost of the first 996 coins.

$1.19 X 83 = $98.77

Then we added the remaining 5 coins, which cost $0.42

$98.77 + $0.42 = $99.19

Therefore, there is a total of $99.19 on the table.

Since, the lowest common multiple of 2, 3, and 4 is 12, the pattern will repeat itself every 12th coin.

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

~

the first one

step-by-step explanation:

just id the test.