+0

Plato Classroom Question #4

+1
4001
4
+112

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 \(39\)?

Nov 15, 2017
edited by SpaceModo  Nov 30, 2017

#1
+326
+1

27? i just chose a random answer...

Nov 15, 2017
#3
+129799
+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

Nov 15, 2017