Question

Based on the equation Y=4.29+143.3X, sales(Y) is in units of $10,000 and advertising(X) is in units of $100. What are sales when $4,497 is spent on advertising?

Answer 1

To find the sales (Y) when $4,497 is spent on advertising, we first need to convert the advertising expenditure into the units specified in the equation, which is in units of $100.

1. **Convert $4,497 to units of $100:**
\[
X = \frac{4497}{100} = 44.97
\]

2. **Substitute X into the equation:**
\[
Y = 4.29 + 143.3 \cdot X
\]
\[
Y = 4.29 + 143.3 \cdot 44.97
\]

3. **Calculate \(143.3 \cdot 44.97\):**
\[
143.3 \cdot 44.97 \approx 6435.721
\]

4. **Now substitute that back into the equation for Y:**
\[
Y \approx 4.29 + 6435.721 \approx 6439.011
\]

5. **Thus, the sales in units of $10,000 is approximately:**
\[
Y \approx 6439.011
\]

To express this in actual dollars, we multiply by 10,000:
\[
\text{Sales} \approx 6439.011 \times 10,000 \approx 64,390,110
\]

Therefore, when $4,497 is spent on advertising, the sales are approximately **$64,390,110**.