Let's analyze each statement individually, given that Alexia spends 3 minutes on each math problem and 4 minutes on each science problem. She aims to surpass 60 minutes in total. We need to evaluate if each pair of math ([tex]$x$[/tex]) and science problems ([tex]$y$[/tex]) exceeds the 60-minute mark using the inequality [tex]\(3x + 4y > 60\)[/tex]. Here are the details:
1. Alexia completed 8 math problems and 9 science problems.
Calculation:
[tex]\[
3(8) + 4(9) = 24 + 36 = 60
\][/tex]
The total time is exactly 60 minutes, which does not satisfy the inequality [tex]\(3x + 4y > 60\)[/tex].
2. Alexia completed 4 math problems and 6 science problems.
Calculation:
[tex]\[
3(4) + 4(6) = 12 + 24 = 36
\][/tex]
The total time is 36 minutes, which does not satisfy the inequality [tex]\(3x + 4y > 60\)[/tex].
3. Alexia completed 20 math problems and 10 science problems.
Calculation:
[tex]\[
3(20) + 4(10) = 60 + 40 = 100
\][/tex]
The total time is 100 minutes, which exceeds 60 minutes and satisfies the inequality [tex]\(3x + 4y > 60\)[/tex].
4. Alexia completed no math problems and 15 science problems.
Calculation:
[tex]\[
3(0) + 4(15) = 0 + 60 = 60
\][/tex]
The total time is exactly 60 minutes, which does not satisfy the inequality [tex]\(3x + 4y > 60\)[/tex].
Thus, the only statement that could be true in this situation is:
Alexia completed 20 math problems and 10 science problems.
