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Jeremy has some stamps to give to his friends. If he gives each friends 2 stamps, Jeremy will have 6 stamps left. It he gives each friend 3 stamps, he will be short of 1 stamp. How many stamps does he have?

1) 20

2) 19

3) 18

4) 17

 Aug 6, 2023
 #1
avatar+129742 
+1

Let F be the number of friends and S be the total number of  stamps.....we have these equations :

 

S - 2F  = 6   

S - 3F  = -1       ("short 1" means  negative 1 )

 

Multiply the first equation by 3  and the second equation by -2

 

3S - 6F  = 18

-2S +6F =  2       add these

 

S  =  20

 

So.....he has 20 stamps  and he has   20 - 2F = 6   →  2F = 20 - 6 →  2F = 14  →  7 friends

 

cool cool cool

 Aug 6, 2023
 #2
avatar+13 
0

Let's set up a system of equations based on the given information:

Let "x" be the number of stamps Jeremy initially has.

According to the first condition, if he gives each friend 2 stamps, he will have 6 stamps left: x - 2f = 6, where "f" is the number of friends.

According to the second condition, if he gives each friend 3 stamps, he will be short of 1 stamp: x - 3f = -1.

Now have a system of two equations:
x - 2f = 6

x - 3f = -1

Let's solve this system to find the value of "x" (the number of stamps Jeremy has):

Subtracting equation 2 from equation 1 gives: 
(x - 2f) - (x - 3f) = 6 - (-1)

x - 2f - x + 3f = 6 + 1

f = 7.


 

Now can substitute the value of "f" into either equation 1 or 2 to solve for "x." Let's use equation 1: 
x - 2(7) = 6

x - 14 = 6

x = 6 + 14

x = 20.

Therefore, Jeremy has 20 stamps.

 

So, the correct answer is:

1. 20

 Aug 7, 2023

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