Natalie earns $2.50 for each CD she sells and $3.50 for each DVD she sells. Natalie sold 45 DVDs last year. She earned a total of $780 last year selling CDs and DVDs.

Write an equation that can be used to determine the number of CDs (c) Natalie sold last year. How many CDs did Natalie sell last year? Show all work.

Natalie claims that she can earn more money this year by selling only 1/3 the number of CDs that she sold last year and by tripling the amount of DVDs she sold last year. Is Natalie's claim correct? Use words, numbers, and/or symbols to support your answer.

2.50CD + 3.50(45) = 780

Divide CDs by 3 and multiply DVDs by 3 at above prices to calculate earnings.

2.50CD/3 + 3.50(45)(3) = ?

To solve this problem, let's start by writing an equation to represent the total earnings from selling CDs and DVDs:

Total earnings = (Number of CDs * Earnings per CD) + (Number of DVDs * Earnings per DVD)

Given that Natalie earns $2.50 for each CD she sells and $3.50 for each DVD she sells, the equation becomes:

Total earnings = (2.50 * C) + (3.50 * 45)

We also know that Natalie earned a total of $780 last year by selling CDs and DVDs. Therefore, we can write the equation as:

780 = (2.50 * C) + (3.50 * 45)

To find the number of CDs Natalie sold last year, we can solve this equation for C. Let's simplify the equation:

780 = 2.50C + 157.50

Subtracting 157.50 from both sides of the equation:

780 - 157.50 = 2.50C

622.50 = 2.50C

Dividing both sides by 2.50:

622.50 / 2.50 = C

C = 249

Therefore, Natalie sold 249 CDs last year.

Now let's evaluate Natalie's claim for this year. She says she can earn more money by selling only 1/3 the number of CDs she sold last year and tripling the amount of DVDs she sold last year.

So, this year she would sell (1/3) * 249 CDs = 83 CDs.

And she would sell 3 times the amount of DVDs from last year, which is 3 * 45 = 135 DVDs.

To find the total earnings this year, we can use the same formula:

Total earnings = (Number of CDs * Earnings per CD) + (Number of DVDs * Earnings per DVD)

Total earnings = (2.50 * 83) + (3.50 * 135)

Total earnings = 207.50 + 472.50

Total earnings = 680

Therefore, Natalie would earn $680 this year.

Comparing the earnings from last year ($780) to this year ($680), we can see that Natalie's claim is incorrect. She would actually earn less money this year by following her claim.