Question 539779
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 {{{27*9.45=255.15}}}
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 {{{14.80-9.45=5.35}}}.
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
{{{281.90-255.15=26.75}}}
At 5.35 per 5kg packet of yummy rice, that correspond to {{{26.75/5.35=5}}}
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
{{{x+y=27}}}
The total cost is
{{{9.45x+14.80y=281.90}}}
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:
{{{x+y=27}}} ---> {{{x=27-y}}}
and I am going to substitute that expression in the other equation
{{{9.45(27-y)+14.8y=281.90}}} ---> {{{9.45*27-9.45*y+14.8*y=281.90}}} --->
{{{9.45*27+(14.80-9.45)y=281.90}}} ---> {{{255.15+5.35y=281.90}}} ---> {{{5.35y=281.90-255.15}}} ---> {{{5.35y=26.75}}} --> {{{y=26.75/5.35}}}
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
{{{x+y=27}}} ---> {{{9.45(x+y)=9.45*27}}} --> {{{9.45*x+9.45*y=255.15}}}
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
{{{9.45x+14.80y=281.90}}} ---> {{{9.45x+14.80y-(9.45*x+9.45*y)=281.90-255.15}}} --> {{{9.45x+14.80y-9.45*x-9.45*y=26.75}}} --> {{{14.80y-9.45*y=26.75}}} --> {{{(14.80-9.45)y=26.75}}} --> {{{5.35y=26.75}}} --> {{{y=26.75/5.35}}}