Peter begins his kindergarten year able to spell 10 words. He is going to learn to spell 2 new words every day. Which in inequality can be used to determine how many days, d, it takes Peter to be able to spell at least 85 words?

Options

A. `2d+10ge85`
B. `20dle85`
C. `(d+2)+1ge85`
D. `2d-10le85`

Answer

To determine how many days, \( d \), it takes Peter to be able to spell at least 85 words, we can set up an inequality based on the information provided.

1. **Identify the initial number of words Peter can spell**:
Peter starts with 10 words.

2. **Determine the rate at which Peter learns new words**:
Peter learns 2 new words every day. Therefore, after \( d \) days, he will have learned \( 2d \) new words.

3. **Set up the inequality**:
To find out how many words Peter can spell after \( d \) days, we combine the words he already knows with the new words he learns. This can be expressed as:
\[ \text{Total words} = \text{Initial words} + \text{New words} = 10 + 2d \]
We want this total to be at least 85 words. Therefore, we set up the inequality:
\[ 10 + 2d \geq 85 \]

4. **Final inequality**:
The inequality that represents the situation is:
\[ 2d + 10 \geq 85 \]

Thus, the inequality that can be used to determine how many days \( d \) it takes Peter to be able to spell at least 85 words is:
\[ 2d + 10 \geq 85 \]