How much does a key ring cost? and How much does a wallet cost?

Question

at freemans office supply , richard bought seven keyrings and two wallets for 165$. The same day , dale bought one keyring and five wallets for 99$ how much does a keyring cost? how much does a wallet cost?

Answer 1

Given,

Richard bought 7 Key rings and 2 Wallets for 165$

Let us Assume Key Ring as K and Wallet as W

we can wrire equation I as - 7k+2W=165- ------------------ I

similarly

dale bought one keyring and five wallets for 99$- II

we can wrire equation I as k+5W=99------------------------- II

here we have to linear equations I and II,solving these two

7k+2W=165

(k+5W=99)-- Multiply with 7 on both sides (Muliplying same number on both sides does not change the value)

k*7+5W*7=99*7 which is equal to 7k+35w=693---------------III

Now solving I and III

7k+2W=165

7k+35w=693

(-)Subtracting These two euations

---------------------------

33W=528

W=16

By substituting W=16 in euation II we get

k+5*16=99

k+80=99

k=19

Therefore The cost of ,the KeyRing is 19$

And Wallet is 16$