To find two other decimals that Holland could have added to 0.34 to make a sum of 2.1, we can first determine what the sum of the two additional decimals should be.
The equation can be set up as follows:
\[ 0.34 + x + y = 2.1 \]
Where \( x \) and \( y \) are the two other decimals. To find \( x + y \), we can subtract 0.34 from 2.1:
\[ x + y = 2.1 - 0.34 \] \[ x + y = 1.76 \]
Now we need to find any two decimal numbers \( x \) and \( y \) that add up to 1.76. There are infinitely many pairs of decimals that satisfy this equation. Here are a couple of examples:
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Example 1:
- Let \( x = 1.00 \)
- Then \( y = 1.76 - 1.00 = 0.76 \)
- In this case, \( x = 1.00 \) and \( y = 0.76 \) are valid decimals because \( 1.00 + 0.76 = 1.76 \).
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Example 2:
- Let \( x = 0.80 \)
- Then \( y = 1.76 - 0.80 = 0.96 \)
- Here, \( x = 0.80 \) and \( y = 0.96 \) are also valid decimals since \( 0.80 + 0.96 = 1.76 \).
Both pairs of decimals (1.00 and 0.76, or 0.80 and 0.96) satisfy the condition that they sum with 0.34 to give 2.1. Therefore, any pairs of decimals that add up to 1.76 can be considered valid answers.
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