James sold magazine subscriptions with three prices: $26, $19, $ 23. He sold 3 fewer of the $26 subscriptions than of the $19 subscriptions and sold a total of 32 subscriptions. If his total of sales amounted to $716, how many $23 subscriptions did James sell?
Ace Rent a Car charges a flat fee of $15 and $0.25 a mile for their cars. Acme Rent a Car charges a flat fee of $30 and $0.17 a mile for their cars. Use the following model to find out after how many miles Ace Rent a Car becomes more expensive than Acme Rent a Car. c= 15+0.25m Ace, c=30+0.17m Acme
Can someone please help me with these two problems?
15 + 0.25m > 30 + 0.17m.
0.25m - 0.17m > 30 - 15,
0.08m > 15,
m > 187.5 Miles.
Sure! I can help you with both of these problems.
Problem 1: James sold magazine subscriptions with three prices: $26, $19, and $23. He sold 3 fewer of the $26 subscriptions than of the $19 subscriptions and sold a total of 32 subscriptions. His total sales amounted to $716. We need to find out how many $23 subscriptions James sold.
To solve this problem, let's set up an equation. Let's say James sold x subscriptions of $19, y subscriptions of $26, and z subscriptions of $23.
According to the problem, James sold 3 fewer of the $26 subscriptions than the $19 subscriptions. So, the equation becomes:
y = x - 3
We also know that the total number of subscriptions is 32, so we have another equation:
x + y + z = 32
Finally, we know that the total amount of his sales was $716, so we have one more equation:
19x + 26y + 23z = 716
Now, we have a system of three equations. To solve it, we can use a method like substitution or elimination.
Problem 2: Ace Rent a Car charges a flat fee of $15 and $0.25 a mile for their cars. Acme Rent a Car charges a flat fee of $30 and $0.17 a mile for their cars. We need to find out after how many miles Ace Rent a Car becomes more expensive than Acme Rent a Car.
We are given the models for both car rentals:
Ace: c = 15 + 0.25m
Acme: c = 30 + 0.17m
In these models, c represents the cost and m represents the number of miles driven.
To find out after how many miles Ace becomes more expensive than Acme, we need to set up an equation and solve for m.
Setting the costs equal to each other, we have:
15 + 0.25m = 30 + 0.17m
Now, let's solve this equation to find the value of m. We can start by isolating the m term by subtracting 0.17m from both sides:
0.25m - 0.17m = 30 - 15
0.08m = 15
To isolate m, we divide both sides by 0.08:
m = 15 / 0.08
Simplifying this expression, we have:
m = 187.5
So, Ace Rent a Car becomes more expensive than Acme Rent a Car after 187.5 miles.
I hope this helps! Let me know if you have any further questions.