Question

question 13 3 pts angela is taking a math exam and needs to complete at least 10 geometry and algebra problems within 2 hours. given angelas proficiency in these two subjects, it will take her 30 minutes to complete the solution for a geometry problem, and 10 minutes to complete the solution for an algebra problem. below, the variable a represents the number of algebra problems, and the variable g represents the number of geometry problems. enter an appropriate value in each blank box below to complete the system of inequalities that define the constraints described above in the problem statement. please note: where applicable, to indicate ≥ enter >=, and to indicate ≤ enter <=

Explanation:

Step1: Total problems constraint

Angela needs at least 10 problems, so \( A + G \geq 10 \). Coefficients of \( A \) and \( G \) are 1, symbol is >=.

Step2: Time constraint

2 hours = 120 minutes. Algebra takes 10 min/problem, geometry 30 min/problem. Total time ≤ 120: \( 10A + 30G \leq 120 \). Coefficients are 10 (A), 30 (G), symbol is <=.

Answer:

1, 1, >=
10, 30, <=