Pregunta
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2b.) The students in Naomi's class earned \( 20 \% \) of the selling price of each calendar sold this year and last year. . At last year's selling price, Naomi's class sold 650 calendars. Fill in the blanks to correctly complete the statement. The students in Naomi's class earned more money by \( \$ 28 \). 800 calendars.

Ask by Donnelly Young. in the United States
Mar 12,2025

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The students in Naomi's class earned more money by $28.800 when they sold 800 calendars this year compared to last year.

Solución

Let's denote the selling price of each calendar as \( x \) dollars. Given that the students in Naomi's class earned \( 20\% \) of the selling price of each calendar sold this year and last year, we can express the amount earned by the students in Naomi's class as \( 0.20x \) dollars per calendar. Last year, Naomi's class sold 650 calendars, so the total amount earned by the students in Naomi's class last year is \( 0.20x \times 650 \) dollars. This year, Naomi's class sold 800 calendars, so the total amount earned by the students in Naomi's class this year is \( 0.20x \times 800 \) dollars. The statement mentions that the students in Naomi's class earned more money by $28.800 calendars. This means that the difference in the total amount earned by the students in Naomi's class between this year and last year is $28.800. We can set up the equation based on the information provided: \[ 0.20x \times 800 - 0.20x \times 650 = 28.800 \] Now, we can solve this equation to find the value of \( x \), which represents the selling price of each calendar. Solve the equation by following steps: - step0: Solve for \(x\): \(0.2x\times 800-0.2x\times 650=28.8\) - step1: Simplify: \(30x=28.8\) - step2: Divide both sides: \(\frac{30x}{30}=\frac{28.8}{30}\) - step3: Divide the numbers: \(x=\frac{24}{25}\) The selling price of each calendar is $0.96. Now, we can calculate the total amount earned by the students in Naomi's class last year and this year: Last year: \( 0.20 \times 0.96 \times 650 = \$ 129.60 \) This year: \( 0.20 \times 0.96 \times 800 = \$ 153.60 \) The difference in the total amount earned by the students in Naomi's class between this year and last year is indeed $28.800, as stated in the problem.

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Beyond the Answer

Last year, at the selling price of each calendar, Naomi's class earned a total of \( 0.20 \times 650 \times \text{price} \). This year, if the selling price increased leading them to sell 800 calendars, their earnings would be \( 0.20 \times 800 \times \text{new price} \). The difference in their earnings, given they earned $28 more this year, can be expressed in an equation: \( 0.20 \times 800 \times \text{new price} - 0.20 \times 650 \times \text{price} = 28 \). Thus, after finding the new selling price and performing some simple calculations, we can conclude that the students in Naomi's class earned $28 more this year by selling an additional 150 calendars!

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