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Principal Perry ordered 50 cupcakes from Cocoa Cups Bakery for his monthly honor roll party. Since this was a bulk order, Cocoa Cups reduced the price of each cupcake by \( \$ 0.60 \). Principal Perry paid \( \$ 95 \) in all. How much does Cocoa Cups normally charge for a cupcake?

Ask by Osborne Rodriguez. in the United States
Dec 03,2024

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Tutor-Verified Answer

Answer

The normal price of each cupcake is $2.50.

Solution

Let \( x \) be the normal price of each cupcake. Since Cocoa Cups reduced the price by \( \$ 0.60 \) for the bulk order, the price per cupcake for this order is \( x - 0.60 \). Principal Perry ordered 50 cupcakes, so the total cost for the cupcakes can be expressed as: \[ 50(x - 0.60) = 95 \] Now, we can distribute the 50: \[ 50x - 30 = 95 \] Next, we add 30 to both sides to isolate the term with \( x \): \[ 50x = 95 + 30 \] \[ 50x = 125 \] Now, we divide both sides by 50 to solve for \( x \): \[ x = \frac{125}{50} = 2.5 \] Thus, the normal price of each cupcake is \[ \boxed{2.50} \]

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Bonus Knowledge

To find out the normal price of a cupcake, we can set up an equation based on the information given. Let's denote the normal price of a cupcake as \( x \). Since Cocoa Cups reduced the price by \( \$ 0.60 \) for this bulk order, the price per cupcake for this order became \( x - 0.60 \). Therefore, for 50 cupcakes, the total cost can be expressed as: \[ 50(x - 0.60) = 95 \] Now, let's solve for \( x \): \[ 50x - 30 = 95 \] \[ 50x = 95 + 30 \] \[ 50x = 125 \] \[ x = \frac{125}{50} \] \[ x = 2.50 \] Thus, Cocoa Cups normally charges \( \$ 2.50 \) for a cupcake! For the fun factor, did you know that cupcakes have a rich history dating back to the 19th century? They gained popularity in the United States in the 1820s, initially referred to as "number cakes" because the ingredients were measured by the cup! Talk about a recipe with a little slice of history! Now, think about the real-world impact of bulk purchasing. Sometimes, customers forget to ask for group discounts when ordering multiple items. Next time you’re planning an event, don’t hesitate to inquire about bulk pricing! Saving money can be both smart and sweet!

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