Let's denote the three decimals that Holland added as \(d_1\), \(d_2\), and \(d_3\). According to the problem, one of these decimals is \(d_1 = 0.34\), and we want the total sum to equal 2:
\[ d_1 + d_2 + d_3 = 2 \]
Substituting \(d_1\):
\[ 0.34 + d_2 + d_3 = 2 \]
To find \(d_2 + d_3\), we can rearrange the equation:
\[ d_2 + d_3 = 2 - 0.34 \]
Calculating the right-hand side:
\[ d_2 + d_3 = 1.66 \]
Now, we need to find two decimals \(d_2\) and \(d_3\) that add up to 1.66. There are many possible pairs for \(d_2\) and \(d_3\). Here are a couple of examples:
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Example 1: Let’s say we choose \(d_2 = 1.00\):
\[ d_3 = 1.66 - 1.00 = 0.66 \]
So, one possible pair of decimals is \(d_2 = 1.00\) and \(d_3 = 0.66\).
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Example 2: Now let's choose \(d_2 = 0.80\):
\[ d_3 = 1.66 - 0.80 = 0.86 \]
Another possible pair is \(d_2 = 0.80\) and \(d_3 = 0.86\).
Both pairs meet the requirement that \(d_2 + d_3 = 1.66\), and therefore, when added to \(d_1 = 0.34\), the sum is:
\[ 0.34 + 1.00 + 0.66 = 2 \quad \text{and} \quad 0.34 + 0.80 + 0.86 = 2 \]
In conclusion, any pair of decimals that fulfills \(d_2 + d_3 = 1.66\) qualifies.
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