3. LaShawn wants to buy some music online. There are two plans to choose from. The first plan is a flat rate of \( \$ 1.29 \) per download. The second plan has a membership fee of \( \$ 21 \) and a fee of \( \$ .99 \) per download. Let \( x \) be the number of downloads and \( C \) be the cost. Plan 1: \( C=1.29 x \) Plan 2: \( C=21+0.99 x \) \( \begin{array}{l}\text { a. When are the costs of the two plans equal to each other? Explain. }\end{array} \)

To find out when the costs of the two plans are equal, set the equations equal to each other: \[ 1.29x = 21 + 0.99x \] Now, subtract \( 0.99x \) from both sides: \[ 1.29x - 0.99x = 21 \] This simplifies to: \[ 0.30x = 21 \] Next, divide both sides by \( 0.30 \): \[ x = \frac{21}{0.30} = 70 \] So, the costs of the two plans are equal when LaShawn downloads 70 songs. At this point, he would spend \( \$ 90.30 \) on both plans (since \( 1.29 \times 70 = 90.30 \) and \( 21 + 0.99 \times 70 = 90.30 \)). Switching gears, let’s think about how this applies to smart spending. If LaShawn expects to download more than 70 songs, the membership plan could save him money, while under 70, he might want to stick with the per-download option. Always calculate your break-even point to determine the most cost-effective solution based on your needs!