can someone correct this for me.
Business and finance. The cost for a long-distance telephone call is $0.36 for the first minute and $0.21 for each additional minute or portion thereof. Write an inequality representing the number of minutes a person could talk without exceeding $3.
Let x = be the number of minutes:
The first minute cost $0.36
The remaining x –1 minutes cost $0.21 each
So the remaining x- 1 minutes altogether costs $0.21 (x – 1)
Total cost = $0.36 + $0.21 (x – 1)
This must be less than or equal $3.00. So we have:
$0.36 +$0.21 (x- 1) <= $ 3.00
Multiply through by 100 and drop the $’s
36 + 21(x –1)<= 300
12 + 7 (x –1)<= 100 (In this step in order to get this equation I had to divide both sides by 3 to make the numbers smaller.)
12 + 7x – 7 <= 100
7x + 5 <=100
To correct the inequality, let's go through the steps:
1. The first mistake is in the step "Total cost = $0.36 + $0.21 (x – 1)." It should be "Total cost = $0.36 + $0.21x - $0.21" because each additional minute costs $0.21, not $0.21 (x – 1).
2. The second mistake is in the inequality "$0.36 +$0.21 (x- 1) <= $ 3.00." It should be "$0.36 + $0.21x - $0.21 <= $ 3.00" because we already corrected the Total cost equation in the previous step.
3. To eliminate the decimals, multiply through the inequality by 100: 100 * ($0.36 + $0.21x - $0.21) <= 100 * $3.00. Simplifying this gives 36 + 21x - 21 <= 300.
4. In the next step, you tried to divide both sides by 3 to make the numbers smaller, but that's not necessary. Instead, let's simplify the inequality further: 36 + 21x - 21 <= 300. Combining like terms gives 7x + 15 <= 300.
5. Finally, simplify the inequality by subtracting 15 from both sides: 7x + 15 - 15 <= 300 - 15. This gives the correct inequality: 7x <= 285.
So, the corrected inequality is 7x <= 285.