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Question 539779: financial;Kirti spent rs.281.90 on a total of 27 packets of australian yummy and healthy rice.[australian yummy rice sells at 9.45 per 5 kg packet and healthy rice at 14.80 per 8 kg packet]calculate the number of weeks her family would take to finish the rice if they eat 1/2 kg of rice everyday?
a.321/2 b. 42 6/7 c.52 1/4 d.none of these.
I solved it using GUESS AND CHECK of problem solving method since algebra was not included for my class of five[India] i did this way.first I must find how many 5 kg packets and 8 kg packets are there in the total 27 packets.I adjust the individual price to the total amount spent with total bags linearly working out from my first guess as 8 kg 9 packets and 5 kg remaining 18 packets and total the amount.I increased 5 kg one packet at a time and 8 kg is reduced one at a time.thus my 5 kg of 8 kg packets and 22 of 5 kg packets were found to be matching with the total amount 281.90/then i calculated the total kg in 5 packets and 22 packets and found that as 150 k.g.then if 1/2 kg -1day ,150 kg would come to 3oo days.divided by 7 i got 42 6/7weeks.my point is it is an international competition exam where the method is not written but correct solution is found. can you tell me whether this guess and check[international problem solving strategy is used elsewhere in exam where solutions are important?besides can you give me the starting equation to work on.sorry for taking your valuable time.I will be really grateful,if you could guide me here.thank you
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! Your solution is correct.
For a multiple choice question where you do not need to show your work, you want the fastest way to the answer that you can feel comfortable with.
Guess and check is OK, but it may be slow if you are not lucky.
If you had been studying algebra, you could set up a system of equations and solve it.
There is another way, one that I would use myself. It is a WHAT-IF way, and works like this:
What if Kirti just wanted to buy 27 packages of the 5kg yummy rice?
That would cost 
What if Kirti thought about replacing one package of the healty rice for one of those 27 packages of yummy rice?
Replacing one packet of 5kg yummy rice with one 8kg packet of healthy rice would increase the total cost by  .
Replacing two packages would increase the cost by twice that, replacing 3 would increase it by 3 times that, and so on.
If the total cost was 281.90, that is an increase over 255.15 of
At 5.35 per 5kg packet of yummy rice, that correspond to 
So I get the number of packets without the guess and check, and I have a clear understanding of what my calculations mean.
With algebra, you would end up doing the same calculations (or similar ones), but less words and more x and y variables would be involved. Often you would get involved in the mechanics of the procedure to the point of losing track of what the calculations really mean.
You would say:
Let x be the number of 5kg packages of yummy rice bought.
Let y be the number of 8kg packages of healthy rice bought.
The total number of packages is
The total cost is
The procedures taught to solve such a system of linear equations are called substitution and elimination.
SUBSTITUTION
You would think, I'm going to transform the first equation to get an expression for x or for y:
---> 
and I am going to substitute that expression in the other equation
 --->  --->
 --->  --->  --->  --> 
ELIMINATION
You would think, I can multiply one of those equations by a number and get an equivalent equation, that would have the same solutions, so
--->  --> 
The expressions on the left and right of the equal sign are the same number, and if I subtract the same number from both sides of an equation I get an equivalent equation, that would have the same solutions, so
--->  -->  -->  -->  --> -->
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