Question

bodhi has a collection of 175 dimes and nickels. the collection is worth $13.30. which equation can be used to find n, the number of nickels in the collection?
○ 0.1n + 0.05(n - 175) = 13.30
○ 0.1n + 0.05(175 - n) = 13.30
○ 0.1(n - 175) + 0.05 = 13.30
○ 0.1(175 - n) + 0.05n = 13.30

Explanation:

Step1: Define variables

Let \( n \) be the number of nickels. Then the number of dimes is \( 175 - n \) (since total coins are 175).

Step2: Calculate value of nickels and dimes

Value of a nickel is \( \$0.05 \), so value of \( n \) nickels is \( 0.05n \).
Value of a dime is \( \$0.10 \), so value of \( (175 - n) \) dimes is \( 0.1(175 - n) \).

Step3: Total value equation

Total value is sum of value of nickels and dimes, so \( 0.1(175 - n) + 0.05n = 13.30 \).

Answer:

\( 0.1(175 - n) + 0.05n = 13.30 \) (the fourth option: \( 0.1(175 - n) + 0.05n = 13.30 \))