Question 29748
Ed and Dave are going to divide a cash prize of $14,000 in a ratio of 2 to 5.  How much will Dave receive?

Let Ed’s share be $A
and let Dave’s share be $B
A+B = 14000----(1)
A/B= 2/5 which implies 
5A = 2B ----(2)
(1) gives B = (14000-A) ----(*)
Using (*) in (2)
5A = 2(14000-A)
5A = 28000-2A
5A+2A = 28000
7A = 28000
A = 28000/7 = 4000
Putting  A = 4000 in (*),we have 
B = 14000-4000 = 10000
Answer: Ed’s share = $4000 and Dave’s share=$10000
Vrification: (4000+10000) = 14000 and 4000/10000 = 4/10 = 2/5 which is correct
Note: If you are not required to do this problem in the form solving of two linear equations in two unknowns you may do this problem orally
The ratio of Ed’s and Dave’s shares is 2: 5 means out of every (2+5=) 7 dollars 
Ed gets $2 and Dave gets $5
And there are (14000/7) = 2000 sevens in the total amount $14000
Therefore Rd’s share is 2X2000 = $4000 and 
Dave’s share is 5X2000 = $10000.
Simple -is n’t it?