Question

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). Four white chocolate truffles (W) cost the same as three dark chocolate truffles (D). If the parent bought 8 white chocolate truffles(W) and 10 dark chocolate truffles (D), and spent $50.00, how much was each dark chocolate truffle?2.422.343.13

Answer 1

Each dark chocolate truffle costs approximately $3.13.

Step-by-step explanation:

To find the cost of each dark chocolate truffle, we can set up a ratio using the information given. Let's assume that the cost of each white chocolate truffle is represented by W, and the cost of each dark chocolate truffle is represented by D.

We know that 4 white chocolate truffles cost the same as 3 dark chocolate truffles. So we can set up the following equation:

4W = 3D

We also know that the parent bought 8 white chocolate truffles and 10 dark chocolate truffles, and spent $50.00. So we can set up another equation:

8W + 10D = 50

We now have a system of two equations:

4W = 3D

8W + 10D = 50

We can solve this system of equations using substitution or elimination. Let's use substitution:

From the first equation, we can solve for W in terms of D:

W = (3/4)D

Substitute this expression for W in the second equation:

8(3/4)D + 10D = 50

Simplify:

6D + 10D = 50

16D = 50

D = 50/16

D ≈ 3.125

So each dark chocolate truffle costs approximately $3.13.

Answer 2

Given the information on the question tab;

`Let\text{ the price for a white chocolate truffle be W, and the price for a dark chocolate truffle be D;}`
`\begin{gathered} From\text{ the statements made in the question;} \\ 4W=3D-----(1) \\ 8W+10D=50----(2) \end{gathered}`

`\begin{gathered} From\text{ equation \lparen1\rparen;} \\ W=(3D)/(4)-----(3) \\ substituting\text{ W=}(3D)/(4)\text{ into equation \lparen2\rparen} \end{gathered}`
`\begin{gathered} 8*(3D)/(4)+10D=50 \\ 6D+10D=50 \\ 16D=50 \\ D=(50)/(16) \\ D=3.125\approx3.13 \end{gathered}`

Final answer:

Each dark chocolate truffle costs $3.13