Question
Aiden has $15.00 on his copy card. Each time he uses the card to make a photocopy, $0.06 is deducted from his card. Aiden wants to be sure that there will be at least $5.00 left on his card when he is finished. The inequality below relates x, the number of copies he can make, with his copy card balance.
15 minus 0.06 x greater-than-or-equal-to 5
What is the maximum number of copies Aiden can make?
60
83
166
250
15 minus 0.06 x greater-than-or-equal-to 5
What is the maximum number of copies Aiden can make?
60
83
166
250
Answers
GPT-4o mini
To find the maximum number of copies Aiden can make, we can solve the inequality:
\[
15 - 0.06x \geq 5
\]
1. First, subtract 15 from both sides:
\[
-0.06x \geq 5 - 15
\]
\[
-0.06x \geq -10
\]
2. Next, divide both sides by -0.06. Remember that dividing both sides of an inequality by a negative number reverses the inequality sign:
\[
x \leq \frac{-10}{-0.06}
\]
\[
x \leq \frac{10}{0.06}
\]
\[
x \leq \frac{10 \times 100}{6} \quad (\text{to eliminate the decimal})
\]
\[
x \leq \frac{1000}{6} \approx 166.67
\]
Since Aiden cannot make a fraction of a copy, we take the largest whole number that is less than or equal to 166.67, which is 166.
Thus, the maximum number of copies Aiden can make is:
\[
\boxed{166}
\]
\[
15 - 0.06x \geq 5
\]
1. First, subtract 15 from both sides:
\[
-0.06x \geq 5 - 15
\]
\[
-0.06x \geq -10
\]
2. Next, divide both sides by -0.06. Remember that dividing both sides of an inequality by a negative number reverses the inequality sign:
\[
x \leq \frac{-10}{-0.06}
\]
\[
x \leq \frac{10}{0.06}
\]
\[
x \leq \frac{10 \times 100}{6} \quad (\text{to eliminate the decimal})
\]
\[
x \leq \frac{1000}{6} \approx 166.67
\]
Since Aiden cannot make a fraction of a copy, we take the largest whole number that is less than or equal to 166.67, which is 166.
Thus, the maximum number of copies Aiden can make is:
\[
\boxed{166}
\]