A store offers an engine for $34 cash or $5 down and 10 weekly payments of $3. Find the interest rate charged using the direct ratio formula.

To find the interest rate charged using the direct ratio formula, we need to compare the total amount paid (including the down payment) to the cash price of the engine.

Let's start with the down payment and the weekly payments. The down payment is $5, and there are 10 weekly payments of $3 each. So the total amount paid is:

Total amount paid = Down payment + (Number of weekly payments * Weekly payment amount)
$$Total~amount~paid = 5 + (10 * 3)$$

Simplifying this expression:
$$Total~amount~paid = 5 + 30$$
$$Total~amount~paid = 35$$

Now we can compare the total amount paid to the cash price of the engine.

Interest rate = (Total amount paid - Cash price) / Cash price * 100%
$$Interest~rate = \frac{Total~amount~paid - Cash~price}{Cash~price} * 100\%$$

In this case, the cash price of the engine is $34, so we can substitute the values into the formula:

$$Interest~rate = \frac{35 - 34}{34} * 100\%$$

Simplifying the expression:
$$Interest~rate = \frac{1}{34} * 100\%$$

Converting the fraction to a decimal:
$$Interest~rate = 0.0294 * 100\%$$

Calculating the percentage:
$$Interest~rate = 2.94\%$$

Answer: The interest rate charged using the direct ratio formula is 2.94%.