Question

ava has some pennies and some nickels. she has at most 20 coins worth a minimum of $0.48 combined. write a system of linear inequalities to represent the situation. answer attempt 1 out of 2 0.01x + 0.05y \boxed{} \boxed{} x + y \boxed{} \boxed{}

Explanation:

Step1: Define Variables

Let \( x \) be the number of pennies and \( y \) be the number of nickels.

Step2: Coin Quantity Inequality

The total number of coins is at most 20, so \( x + y \leq 20 \).

Step3: Coin Value Inequality

Pennies are worth $0.01$ each, nickels $0.05$ each, and total value is at least $0.48$. So \( 0.01x + 0.05y \geq 0.48 \).

Step4: Non - negative Constraints

Since the number of coins can't be negative, \( x \geq 0 \) and \( y \geq 0 \) (and \( x,y \) are integers, but for inequalities, non - negative reals first).

Answer:

The system of linear inequalities is:
\( x + y \leq 20 \)
\( 0.01x + 0.05y \geq 0.48 \)
\( x \geq 0 \)
\( y \geq 0 \)