Question

1. isabella has some dimes and some quarters. she has at most 25 coins worth a minimum of $4.45 combined. write a system of inequalities to determine all possible values for the number of quarters (q) and dimes (d) that isabella could have.

options:

• (d + q < 25), (0.10d+0.25q > 4.45)
• (d + q > 25), (0.10d + 0.25q < 4.45)
• (d + qgeq25), (0.10d + 0.25qgeq4.45)
• (d + qleq25), (0.10d + 0.25qgeq4.45)

Explanation:

Step1: Analyze the number - of - coins condition

She has at most 25 coins. So the sum of the number of dimes ($d$) and quarters ($q$) should be less than or equal to 25. The inequality is $d + q\leq25$.

Step2: Analyze the value - of - coins condition

A dime is worth $0.10$ dollars and a quarter is worth $0.25$ dollars. The combined value of her coins is at least $4.45$ dollars. So the inequality is $0.10d + 0.25q\geq4.45$.

Answer:

$d + q\leq25$
$0.10d + 0.25q\geq4.45$ (corresponding to the last option in the multiple - choice list)