SOLUTION: Mwikali planned to spend sh. 16,800 to buy a number of bags of maize. When she went to the market she discovered that the price of maize had increased by sh. 200 per bag. She could

Algebra ->  Finance -> SOLUTION: Mwikali planned to spend sh. 16,800 to buy a number of bags of maize. When she went to the market she discovered that the price of maize had increased by sh. 200 per bag. She could      Log On


   

Question 1153420: Mwikali planned to spend sh. 16,800 to buy a number of bags of maize. When she went to the market she discovered that the price of maize had increased by sh. 200 per bag. She could now afford to buy two bags less than she had planned to buy with the same amount of money.
(a) Determine the number if bags she had planned to buy.
(b)Find how much she paid per bag after the increase in price.
(c)she later sold the maize at sh. 1,750 per bag. Find the percentage profit she made.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
Plan was to buy b bags of maize.
p, the price per bag (for the planned purchase)
                PRICE            QUANTITY         COST 

PLAN             p                 b              16800

DONE            p+200             b-2             16800



A better arrangement of the information:


                PRICE            QUANTITY         COST 

PLAN             p                 16800/p        16800

DONE            p+200           16800/(p+200)     16800

DIFFERENCE                         2

highlight_green%2816800%2Fp-16800%2F%28p%2B200%29=2%29

Answer by ikleyn(52852) About Me  (Show Source):
You can put this solution on YOUR website!
.

            The equation written in the post by @josgarithmetic was INCORRECT, and the problem COULD NOT be solved in this way.

            So, I came to provide the correct solution. 


Let x be the number of bags he planned to buy.


Then the price for each bag before increasing would be  16800%2Fx.


After increasing, the price for each bag was  16800%2F%28x-2%29.


The difference in prices is 200 per bag.  It gives you an equation


    16800%2F%28x-2%29 - 16800%2Fx = 200.


You can solve this problem algebraically, reducing to quadratic equation.


But there is easy way to solve it mentally.


You need to find the factors of the number 16800 that differ in 2 units and produce the quotients that differ in 200 units.


Notice that 168 = 12*14;  so, check the factors 12 and 14


    16800%2F12 = 1400;  16800%2F14 = 1200  and  1400-1200 = 200.


So, x = 14  is your ANSWER

Solved.

Do the rest of the assignment on your own.

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After seeing my post, @josgarithmetic fixed/changed his equation . . .