Write the following comparison as a ratio reduced to lowest terms.
34 nickels to 10 dimes
\(\boxed{17:10}\) is the final answer.
Step 1 :Write the following comparison as a ratio reduced to lowest terms: 34 nickels to 10 dimes.
Step 2 :To solve this problem, we need to convert the nickels and dimes to their monetary value in cents. A nickel is worth 5 cents and a dime is worth 10 cents.
Step 3 :Then, we can write the ratio of their values and reduce it to lowest terms.
Step 4 :Calculate the value of nickels: \(34 \times 5 = 170\) cents.
Step 5 :Calculate the value of dimes: \(10 \times 10 = 100\) cents.
Step 6 :Calculate the greatest common divisor (gcd) of the values of nickels and dimes, and then use it to reduce the ratio to its lowest terms.
Step 7 :The ratio of 170 to 100, reduced to lowest terms, is \(17:10\).
Step 8 :\(\boxed{17:10}\) is the final answer.