A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 points each and multiple choice questions worth 11 points each. How many multiple choice questions are on the test?
Let's assume there are x multiple choice questions on the test.
So, there are 20 - x True/False questions on the test.
The total score for the multiple choice questions is 11x.
The total score for the True/False questions is 3 * (20 - x).
The total score for the test is 100.
So, the equation becomes 11x + 3 * (20 - x) = 100.
Simplifying the equation, we get 11x + 60 - 3x = 100.
Combining like terms, we get 8x + 60 = 100.
Subtracting 60 from both sides, we get 8x = 40.
Dividing both sides by 8, we get x = 5.
Therefore, there are 5 multiple choice questions on the test. Answer: \boxed{5}.
The Rushwood Elementary School PTA is hosting a “Donuts with Dad” breakfast for the Kindergarten students. They have asked the Donut Factory for pricing to cater the event. Below are two options the Donut Factory provided the PTA:
Package 1: Base fee of $20 plus $1.50 per person
Package 2: $2.50 per person
Let x represent the number of people attending the breakfast, and y represent the total cost of the breakfast. Which of these systems of equations could be used to model the two package options?
Option 1: The base fee of $20 will always be added to the cost per person, which is $1.50. So, the equation for package 1 would be y = 1.50x + 20.
Option 2: The cost is simply $2.50 per person, so the equation for package 2 would be y = 2.50x.
Therefore, the system of equations that could be used to model the two package options is:
y = 1.50x + 20
y = 2.50x