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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

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

1 answer

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).