Question
Liam has 125 postcards. He receives 6 postcards every week. At least how many weeks does he need to have more than 200 postcards?
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16
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14
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11
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13
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16
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14
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11
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13
Answers
GPT-4o mini
To determine how many weeks Liam needs to have more than 200 postcards, we can set up the following equation.
1. Liam currently has 125 postcards.
2. He receives 6 postcards every week.
Let \( x \) be the number of weeks he needs. After \( x \) weeks, he will have:
\[ 125 + 6x \]
We want to find the smallest \( x \) such that:
\[ 125 + 6x > 200 \]
Subtract 125 from both sides:
\[ 6x > 200 - 125 \]
\[ 6x > 75 \]
Now, divide both sides by 6:
\[ x > \frac{75}{6} \]
\[ x > 12.5 \]
Since \( x \) must be a whole number (since we can't have a fraction of a week), we round up to the nearest whole number, which is 13.
Therefore, he needs at least **13 weeks** to have more than 200 postcards.
The answer is \( \boxed{13} \).
1. Liam currently has 125 postcards.
2. He receives 6 postcards every week.
Let \( x \) be the number of weeks he needs. After \( x \) weeks, he will have:
\[ 125 + 6x \]
We want to find the smallest \( x \) such that:
\[ 125 + 6x > 200 \]
Subtract 125 from both sides:
\[ 6x > 200 - 125 \]
\[ 6x > 75 \]
Now, divide both sides by 6:
\[ x > \frac{75}{6} \]
\[ x > 12.5 \]
Since \( x \) must be a whole number (since we can't have a fraction of a week), we round up to the nearest whole number, which is 13.
Therefore, he needs at least **13 weeks** to have more than 200 postcards.
The answer is \( \boxed{13} \).