Question

Pankaj wants to create tests for SAT students. He wants to make some calculator and non calculator tests. He figures that each non-calculator test will take him $3$ hours to create, and each calculator test will take $4$ hours to create. Because of his time constraint, he can at most devote at most $6$ hours per week of his time for the next $5$ weeks to create the practice and he wants to provide at least $8$ practice tests , which of the system of inequality represent how many of each type of test he can create ?

• A. $n+c\ge 83n+4c\le 6$
• B. $n+c\ge 83n+4c\le 30$
• C. $n+c\le 83n+4c\ge 30$
• D. $n+c\ge 63n+4c\le 8$

Answer 1

The correct option is B $n+c\ge 83n+4c\le 30$

Given that non calculator test will take him $3$ hours to create and calculator test will take $4$ hours, but he can at most devote $6$ hours per week of his the next $5$ weeks

And he wants to provide at least $8$ practice test.

Let number of non calculator is $n$ and number of calculator test is $c$

Then number of total test $=n+c$

And total time for non calculator test $=3n$

And total time for calculator test $=4c$

Then total time for non calculator test $+$ calculator test $=3n+4c$

But total test given $=8$

And total time $=$ $6\times 5=30$ hours

So $n+c\ge 8$

$3n+4c\le 30$