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.

How many stamps does John have? \(21\), \(27\), \(30\), or \(39\)?

SpaceModo
Nov 15, 2017

#3**+3 **

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.

Call the number that Johan has = x....and the number that Jonathan has = y so x = y

Call the number of stamps that John has = z ......so...we have these two additional equations

2x + 11 = 5z

3y + 3 = 7z

Since Johan and Jonathan have the same number of stamps, the first equation becomes

2y + 11 = 5z divide both side by 5

[2y + 11 ] / 5 = z sub this into the second equation for z

3y + 3 = 7 [ 2y + 11 ] / 5 multiply both sides by 5

15y + 15 = 7 [ 2y + 11]

15y + 15 = 14y + 77 subtract 15, 14y from both sides

y = 62

Using 2y + 11 = 5z we have that

2(62) + 11 = 5z

124 + 11 = 5z

135 = 5z divide both sides by 5

27 = z = John's stamps

CPhill
Nov 15, 2017