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
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
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