Question

Holland added three decimals that made a sum 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.

(4 points)

Answer 1

To find the two other decimals that Holland could have used to make a sum of 2, we start with the information provided:

1. One of the decimals is \( 0.34 \).
2. We need to find two other decimals, say \( x \) and \( y \), such that

\[
0.34 + x + y = 2.
\]

To isolate \( x + y \), we can subtract \( 0.34 \) from both sides:

\[
x + y = 2 - 0.34.
\]

Calculating the right side gives:

\[
2 - 0.34 = 1.66.
\]

Now we have the equation:

\[
x + y = 1.66.
\]

This equation means that the sum of the two decimals \( x \) and \( y \) must equal \( 1.66 \).

Since there are infinitely many pairs of decimals that can satisfy this equation, we can choose specific values for \( x \) and \( y \). For example:

1. We could let \( x = 1.00 \) and hence \( y = 1.66 - 1.00 = 0.66 \).
2. Another pair could be \( x = 0.80 \) and \( y = 1.66 - 0.80 = 0.86 \).

Thus, two possible pairs of decimals that Holland could have used to make a sum of 2 are:

- \( x = 1.00 \) and \( y = 0.66 \)
- or \( x = 0.80 \) and \( y = 0.86 \).

In summary, any two decimals that add up to \( 1.66 \) alongside \( 0.34 \) will suffice.