Question

Avery uses a blend of dark chocolate and milk chocolate to make the ice cream topping at her restaurant. She wants to buy
\[10\,\text{kg}\] more of dark chocolate than milk chocolate, and she needs
\[150\,\text{kg}\] of chocolate in total for her next order.
Let
\[d\] be the number of kilograms of dark chocolate she buys and
\[m\] be the number of kilograms of milk chocolate she buys.
Which system of equations represents this situation?
Choose 1 answer:
Choose 1 answer:
(Choice A)

\[\begin{cases}
d=m+10
\\\\
d+m=150
\end{cases}\]
A

\[\begin{cases}
d=m+10
\\\\
d+m=150
\end{cases}\]
(Choice B)

\[\begin{cases}
m=10d \\\\
d+m=150
\end{cases}\]
B

\[\begin{cases}
m=10d \\\\
d+m=150
\end{cases}\]
(Choice C)

\[\begin{cases}
m=d+10 \\\\
d+m=150
\end{cases}\]
C

\[\begin{cases}
m=d+10 \\\\
d+m=150
\end{cases}\]
(Choice D)

\[\begin{cases}
d=10m \\\\
d+m=150
\end{cases}\]
D

\[\begin{cases}
d=10m \\\\
d+m=150
\end{cases}\]

Answer 1

To represent the situation mathematically, we have two pieces of information:

1. Avery wants to buy 10 kg more of dark chocolate than milk chocolate.
2. The total amount of chocolate she needs is 150 kg.

Let's define the variables:
- Let \(d\) be the number of kilograms of dark chocolate.
- Let \(m\) be the number of kilograms of milk chocolate.

From the first piece of information, we can formulate the equation:
\[ d = m + 10 \]

From the second piece of information, we can formulate the equation:
\[ d + m = 150 \]

Thus, the system of equations that represents this situation is:
\[
\begin{cases}
d = m + 10 \\
d + m = 150
\end{cases}
\]

Looking at the options provided, this corresponds to **Choice A**:

\[
\begin{cases}
d = m + 10 \\
d + m = 150
\end{cases}
\]

So, the correct answer is **(Choice A)**.