Questions: Activity 3: Nickels Dimes Andre's coin jar contains 85 cents. There are no quarters or pennies in the jar, so the jar has all nickels, all dimes, or some of each. 1. Write an equation that relates the number of nickels, n, the number of dimes, d, and the amount of money, in cents, in the coin jar.

Activity 3: Nickels Dimes
Andre's coin jar contains 85 cents. There are no quarters or pennies in the jar, so the jar has all nickels, all dimes, or some of each.
1. Write an equation that relates the number of nickels, n, the number of dimes, d, and the amount of money, in cents, in the coin jar.

Transcript text: Activily 3: Nickels \& Dimes Andre's coin jar contains 85 cents. There are no quarters or pennies in the jar, so the jar has all nickels, all dimes, or some of each. 1. Write an equation that relates the number of nickels, $n$, the number of dimes, $d$, and the amount of money, in cents, in the coin jar.

Solution

Solution Steps

To solve this problem, we need to create an equation that relates the number of nickels (n), the number of dimes (d), and the total amount of money in cents (85 cents). We know that each nickel is worth 5 cents and each dime is worth 10 cents. Therefore, the total value of the nickels and dimes can be expressed as $5n + 10d = 85$.

Step 1: Define the Equation

We start with the total amount of money in the jar, which is 85 cents. The value of each nickel is 5 cents and the value of each dime is 10 cents. Therefore, we can express the relationship between the number of nickels $ n $ and the number of dimes $ d $ with the equation: \[ 5n + 10d = 85 \]

Step 2: Simplify the Equation

To simplify the equation, we can divide all terms by 5: \[ n + 2d = 17 \]

Step 3: Interpret the Equation

This equation $ n + 2d = 17 $ indicates that for every dime $ d $, the number of nickels $ n $ decreases by 2. This relationship can be used to find various combinations of $ n $ and $ d $ that satisfy the equation, where both $ n $ and $ d $ must be non-negative integers.