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?
I will do the first, you do the second
number of $19's --- x
number of $26's --- x-3
number of $23's --- 32 - x - (x-3) = 35-2x
19x + 26(x-3) + 23(35-2x) = 716
19x + 26x - 78 + 805 - 46x = 716
-x = -11
x = 11
he sold 11 of the $19's
8 of the $26's and
13 of the $23's
Sure! I can help you with these two problems.
First, let's solve the problem about James and the magazine subscriptions.
Let's denote the number of $19 subscriptions sold as x. Therefore, the number of $26 subscriptions sold would be x - 3.
We know that the total number of subscriptions sold is 32, so we can write the equation:
x + (x - 3) + (number of $23 subscriptions) = 32.
Now let's calculate the total sales:
Total sales = (number of $19 subscriptions) * $19 + (number of $26 subscriptions) * $26 + (number of $23 subscriptions) * $23.
And we know that the total sales amounted to $716, so we can write:
716 = x * 19 + (x - 3) * 26 + (number of $23 subscriptions) * 23.
To solve this system of equations, we need to find the values of x and (number of $23 subscriptions) that satisfy both equations.
Next, let's solve the second problem about the car rental fees:
We are given the following equations for the costs:
Ace Rent a Car: c = 15 + 0.25m.
Acme Rent a Car: c = 30 + 0.17m.
We want to find out after how many miles Ace Rent a Car becomes more expensive than Acme Rent a Car.
To determine this, we need to find the point at which the costs are equal, and when Ace Rent a Car's cost surpasses Acme Rent a Car's cost.
We can set up an equation to represent this:
15 + 0.25m = 30 + 0.17m.
Now, we can solve this equation for m to find the number of miles at which Ace Rent a Car becomes more expensive than Acme Rent a Car.