Question

1. grace has $100. she is buying charms for her bracelet that cost $5 each. write an equation showing the relationship between the number of charms, c, she buys and the amount of money she has left, m.
2. use the equation you wrote for exercise 11 to find the number of charms grace can buy before she runs out of money.

4-9 use patterns to write and solve equations 57

Explanation:

Step1: Define total cost of charms

The total cost of $c$ charms is $5c$, since each charm costs $5.

Step2: Relate money left to total

Grace starts with $100, so the money left $m$ is initial money minus total charm cost.
$m = 100 - 5c$

Step3: Set money left to 0

To find when she runs out of money, set $m=0$.
$0 = 100 - 5c$

Step4: Solve for $c$

Rearrange to isolate $c$: $5c = 100$, then $c = \frac{100}{5} = 20$

Answer:

1. Equation: $m = 100 - 5c$
2. Number of charms: 20