Question

A school announces two prizes for \[100\% \] attendance and five prizes for \[95\% \] plus marks in all the subjects. If the total value of prizes is \[Rs.1900\], express the information as a linear combination in two variables.

Answer 1

Hint: We assume the value of two categories of prizes as two different variables and counting the number of prizes to be awarded for each category, we make a linear equation where we multiply number of prizes to the value of each category respectively and add them to give total amount to be rewarded.

Complete step-by-step answer:
We are given two categories of prizes, therefore, we will assume two variables each as one category of prize.
Let, value of category of \[100\% \] attendance be denoted by \[x\]
Value of category of \[95\% \] plus marks in all subjects be denoted by \[y\]
Now we count number of prizes in each category,
Number of prizes for category of \[100\% \] attendance is \[2\]
Number of prizes for category of \[95\% \] plus marks in all subjects is \[5\]
Now, we know total value awarded for category of \[100\% \] attendance prizes will be number of prizes multiplied with value of each prize \[ = 2x\]
Also, we know total value awarded for category of \[95\% \] plus marks in all subjects prizes will be number of prizes multiplied with value of each prize \[ = 5y\]
Therefore, from these equations we can write total value of prizes as sum of value of each prize
Total value of prizes \[ = 2x + 5y\]
We are given the total value of prizes as \[Rs.1900\]
So we equate both the values of total values of prizes
\[2x + 5y = Rs.1900\]
Which is a linear combination in two variables.

Note: Students are likely to make the mistake of making wrong assumptions in these types of questions, they might assume the category as variable but when they will multiply the category with the number of prizes per category they will not get an equation for value.