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Complete the equation.

[tex]
\begin{array}{c}
L = \text{Large Cups} \quad M = \text{Medium Cups} \\
2M + 3L = 26 \\
M + L = [?]
\end{array}
\]

Sagot :

GinnyAnswer
Sure, let's solve this step by step.

Given the system of equations:

[tex]\[ 2M + 3L = 26 \][/tex]

[tex]\[ M + L = X \][/tex]

We know that [tex]\(M\)[/tex] represents the number of medium cups and [tex]\(L\)[/tex] represents the number of large cups.

First, we need to find suitable integer values for [tex]\(M\)[/tex] and [tex]\(L\)[/tex] that satisfy the first equation:

[tex]\[ 2M + 3L = 26 \][/tex]

By examining possible values, we eventually find that when [tex]\(M = 1\)[/tex] and [tex]\(L = 8\)[/tex], the equation balances out:

[tex]\[ 2(1) + 3(8) = 26 \][/tex]
[tex]\[ 2 + 24 = 26 \][/tex]
[tex]\[ 26 = 26 \][/tex]

Thus, the values that satisfy the equation are [tex]\(M = 1\)[/tex] and [tex]\(L = 8\)[/tex].

Now, substituting these values into the second equation:

[tex]\[ M + L = X \][/tex]

[tex]\[ 1 + 8 = 9 \][/tex]

So, [tex]\(M + L = 9\)[/tex].

In conclusion, she used:
- 1 medium cup ([tex]\(M = 1\)[/tex])
- 8 large cups ([tex]\(L = 8\)[/tex])

Therefore, the total number of cups is 9.

The completed equation is:

[tex]\[ M + L = 9 \][/tex]
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