Question

John, Johan, and Jonathan collect postage stamps. Johan and Jonathan have the same number of stamps. Two times Johan’s collection is eleven less than five times John’s collection, and three times Jonathan’s collection is three less than seven times John’s collection.

What is the number of postage stamps in John’s collection?

Answer 1

x = john, y = johan, z = jonathan

y = z
2y = 5x - 11....y = 5/2x - 11/2
3z = 7x - 3...z = 7/3x - 1

5/2x - 11/2 = 7/3x - 1..multiply by 6 to get rid of fractions
15x - 33 = 14x - 6
15x - 14x = -6 + 33
x = 27...so John (x) has 27 stamps in his collection

Answer 2

Let d = number of stamps from John (4 letters, d is 4th letter, etc)
Let e = number of stamps from Johan
Let h = number of stamps from Jonathan

Johan and Jonathan have the same number of stamps, so:

e = h

2 times Johan's collection is 11 less than 5 times John's collection, so:

2e = 5d - 11

3 times Jonathan's collection is 3 less than 7 times John's collection,so:

3h = 7d - 3

Now we have three equations and three unknowns. You're asked for the number of stamps in John's collection, so you want the value to variable "d".

Since e = h, we can substitute "h" for "e" in the second equation.

2h = 5d - 11
3h = 7d - 3

now we have two equations and two unknowns. I'll use elimination, starting with multiplying the first equation by -3 and the second one by 2.

-6h = -15d + 33
6h = 14d - 6

now add both together and you have an equation with one unknown remaining:

0 = -d + 27
d = 27

So your answer is 27 stamps. If you want to know how many stamps the others have, you can work back and solve for e and h.