Rachel sells 60 scones. She sells them to Robbie, Cameron, Louis, Tom and Charlie in that order. Each costumer buys more scones than the last and the increase is the same number in each case. Robbie and Cameron’s combined total number of scones in three sevenths of the total of Louis, Tom and Charlie. How many scones does each boy buy?

Suppose Robbie buys ‘a’ scones.
Let ‘d’ be the increase in number of cones
So Cameron buys a + d
Louis buys a + 2d
Tom buys a + 3d
Charlie buys a + 4d
So
a+ a + d+ a + 2d + a + 3d + a + 4d = 60
5a + 10d = 60
Dividing each term by 5 we get
a + 2d = 12 ....(1)
Also
Robbie’s + Cameron’s scones = [tex] \frac{3}{7} [/tex] of Louis , Charlie & Tom's scones
[tex] a+a+d=\frac{3}{7} (a+2d + a + 3d + a+4d) [/tex]
7(2a+d) = 3(3a+9d)
14a+7d = 9a + 27d
14a-9a = 27d-7d
5a=20d
a= 4d
Substituting in (1)
we get
4d + 2d = 12
6d=12
d= 2
Substituting the value of d in (1)
a + 4 = 12
a= 8
Hence
Robbie buys = 8 scones
Cameron buys = 10 scones
Louis buys = 12 scones
Tom Buys = 14 scones
Charlie buys = 16 scones.