Question

Holland added three decimals that made up some of 2. One of the decimals was 0.34 what are two other decimals Holland could have used to make a sum of 2 explain how you know

Answer 1

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:

1. **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 \(d_3 = 0.66\).

2. **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.