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.

Answer 1

To find the two other decimals that Holland could have used, we start by using the information provided:

1. One of the decimals is 0.34.
2. The sum of all three decimals is 2.

We can set up the equation to find the sum of the two other decimals. Let \( x \) and \( y \) be the other two decimals. We can express this relationship mathematically as:

\[
0.34 + x + y = 2
\]

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

\[
x + y = 2 - 0.34
\]

Calculating the right side:

\[
2 - 0.34 = 1.66
\]

Now we know that the sum of the two other decimals \( x \) and \( y \) must be:

\[
x + y = 1.66
\]

There are many pairs of decimals that can add up to 1.66. Some possible pairs include:

- \( x = 0.80 \) and \( y = 0.86 \) (since \( 0.80 + 0.86 = 1.66 \))
- \( x = 1.00 \) and \( y = 0.66 \) (since \( 1.00 + 0.66 = 1.66 \))
- \( x = 0.50 \) and \( y = 1.16 \) (since \( 0.50 + 1.16 = 1.66 \))

Any combination of decimals that satisfies \( x + y = 1.66 \) is valid.

Thus, Holland could have used, for example, the decimals \( 1.00 \) and \( 0.66 \) or any of the other pairs listed above to achieve a sum of 2 when added to 0.34.