Respuesta :
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.
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.
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
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