Questions: A parent is buying two types of chocolate truffles for the children. The oldest child likes white chocolate (W), the younger two like dark chocolate (D) and the spouse likes white chocolate (W). Three white chocolate truffles (W) cost the same as two dark chocolate truffles (D). If the parent bought 5 white chocolate truffles (W) and 10 dark chocolate truffles (D), and spent 60.00, how much was each dark chocolate truffle? Calculate the cost of dark chocolate truffles. Answer * 4.50 4.00 3.00

A parent is buying two types of chocolate truffles for the children. The oldest child likes white chocolate (W), the younger two like dark chocolate (D) and the spouse likes white chocolate (W). Three white chocolate truffles (W) cost the same as two dark chocolate truffles (D). If the parent bought 5 white chocolate truffles (W) and 10 dark chocolate truffles (D), and spent 60.00, how much was each dark chocolate truffle? Calculate the cost of dark chocolate truffles. Answer * 4.50 4.00 3.00
Transcript text: Apprenti Math Assessment Question 41 of 61 Tired? Need a break? All your answers have been saved. You can close the assessment and use the link in your email to access it when you are ready to start again. A parent is buying two types of chocolate truffles for the children. The oldest child likes white chocolate (W), the younger two like dark chocolate (D) and the spouse likes white chocolate (W). Three white chocolate truffles (W) cost the same as two dark chocolate truffles (D). If the parent bought 5 white chocolate truffles (W) and 10 dark chocolate truffles (D), and spent $\$ 60.00$, how much was each dark chocolate truffle? Calculate the cost of dark chocolate truffles. Answer * $\$ 4.50$ $\$ 4.00$ $\$ 3.00$
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Solution

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Solution Steps

Step 1: Define Variables

Let \( W \) be the cost of one white chocolate truffle, and \( D \) be the cost of one dark chocolate truffle.

Step 2: Set Up Equations

From the problem, we know:

  • Three white chocolate truffles cost the same as two dark chocolate truffles: \[ 3W = 2D \]
  • The total cost for 5 white chocolate truffles and 10 dark chocolate truffles is $60: \[ 5W + 10D = 60 \]
Step 3: Solve the System of Equations

First, solve the equation \( 3W = 2D \) for \( W \): \[ W = \frac{2}{3}D \]

Substitute \( W = \frac{2}{3}D \) into the second equation: \[ 5\left(\frac{2}{3}D\right) + 10D = 60 \]

Simplify and solve for \( D \): \[ \frac{10}{3}D + 10D = 60 \]

Combine the terms: \[ \frac{10}{3}D + \frac{30}{3}D = 60 \]

\[ \frac{40}{3}D = 60 \]

Multiply both sides by 3 to clear the fraction: \[ 40D = 180 \]

Divide by 40: \[ D = \frac{180}{40} = 4.5 \]

Final Answer

The cost of each dark chocolate truffle is \(\boxed{\$4.50}\).

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