Create systems of equations where sublimation will solve it. Show work:
1. All 231 students in the math club went on a field trip some students rode in Vans which hold seven students each and some students rode in buses which hold 25 students each how many of each type of vehicle did they use if there were 15 Vehicles total?
2. At Elisa's printing company LLC there are two kinds of printing presses Model A which can print 70 books per day and model B which can Prince 55 books per day the company owns 14 total printing presses and this allows them to print 905 books per day how many of each type of press do they have?
1. Let's use the variables V and B to represent the number of Vans and Buses used, respectively.
We are given the following information:
V + B = 15 (total number of vehicles)
7V + 25B = 231 (total number of students)
To solve this system of equations using sublimation, we will eliminate one variable by multiplying one or both equations by a suitable constant. In this case, we will eliminate the variable V by multiplying the first equation by 7.
7V + 7B = 105
7V + 25B = 231
Now, subtract the first equation from the second equation:
(7V + 25B) - (7V + 7B) = 231 - 105
18B = 126
B = 7
Substitute this value of B back into the first equation to solve for V:
V + 7 = 15
V = 8
Therefore, there were 8 Vans and 7 Buses used.
2. Let's use the variables A and B to represent the number of Model A and Model B printing presses, respectively.
We are given the following information:
A + B = 14 (total number of printing presses)
70A + 55B = 905 (total number of books)
To solve this system of equations using sublimation, we will eliminate one variable by multiplying one or both equations by a suitable constant. In this case, we will eliminate the variable A by multiplying the first equation by 70.
70A + 70B = 980
70A + 55B = 905
Now, subtract the first equation from the second equation:
(70A + 55B) - (70A + 70B) = 905 - 980
-15B = -75
B = 5
Substitute this value of B back into the first equation to solve for A:
A + 5 = 14
A = 9
Therefore, there are 9 Model A printing presses and 5 Model B printing presses.