Answer:
[tex]\begin{cases}d+m=10\\\\1.2d+m=11.2\end{cases}[/tex]
Step-by-step explanation:
Let d represent the number of ounces of dark chocolate.
Let m represent the number of ounces of milk chocolate.
Beth needs to buy a total of 10 ounces of chocolate for her next order. This can be represented by the equation:
[tex]d + m = 10[/tex]
Given that dark chocolate costs $1.20 per ounce, milk chocolate costs $1.00 per ounce, and Beth wants to spend $11.20 in total, this can be represented by the equation:
[tex]1.20d + 1.00m=11.20\\\\1.2d+m=11.2[/tex]
So, the system of equations that represents the situation is:
[tex]\begin{cases}d+m=10\\\\1.2d+m=11.2\end{cases}[/tex]
[tex]\dotfill[/tex]
To solve the system of equations, rearrange the first equation to isolate m:
[tex]m=10-d[/tex]
Now, substitute this into the second equation and solve for d:
[tex]1.2d+(10-d)=11.2\\\\1.2d+10-d=11.2\\\\0.2d+10=11.2\\\\0.2d=11.2-10\\\\0.2d=1.2\\\\d=\frac{1.2}{0.2}\\\\d=6[/tex]
So, Beth needs to buy 6 ounces of dark chocolate.
Substitute d = 6 into m = 10 - d and solve for m:
[tex]m=10-6\\\\m=4[/tex]
Therefore, Beth needs to buy 4 ounces of milk chocolate.