Math Snap

STEP 1

1. The cost of the notebook before tax is $\$4.50$.
2. The cost of the notebook after tax is $\$4.86$.
3. The sales tax rate is a percentage of the pre-tax cost.

STEP 2

1. Define the variable for the sales tax rate.
2. Set up the equation relating pre-tax cost, tax rate, and post-tax cost.
3. Solve for the sales tax rate.

STEP 3

Let $r$ be the sales tax rate expressed as a decimal.

STEP 4

The total cost after tax is the sum of the pre-tax cost and the tax amount. Set up the equation:
$$4.50 + 4.50 \cdot r = 4.86$$

STEP 5

Subtract the pre-tax cost from both sides to isolate the tax amount:
$$4.50 \cdot r = 4.86 - 4.50$$ Calculate the right-hand side:
$$4.50 \cdot r = 0.36$$

Divide both sides by $4.50$ to solve for $r$:
$$r = \frac{0.36}{4.50}$$ Calculate $r$:
$$r = 0.08$$ Convert $r$ to a percentage:
$$r = 0.08 \times 100\% = 8\%$$ The sales tax rate is:
$$\boxed{8\%}$$