Updated: Aug 31, 2021
An amusement park has an entrance fee of $40 for a day and $3 for each ride in the park. What is the total cost, in dollars, of going on 14 rides in a day at the amusement park?
A) $42
B) $43
C) $70
D) $82
Maps to Category 14 of the book.
Answer posted on 07/25/2021: Correct answer choice is D.
Total cost = entrance fee + cost of 14 rides.
Entrance fee is given as $40.
Cost of each ride is given as $3. Hence, cost of 14 rides is 14 x 3 = 42.
Total cost = 40 + 42 = 82.
Updated: Jul 18, 2021
For what value of the constant c the equation 3(2x + c) = 6x + 2 + c has infinitely many solutions?
Maps to Category 13 of the book.
Answer posted on 07/18/2021: Answer is 1.
For the equation to have infinitely many solutions, expressions on both sides of the equation must be equal. The coefficient of x in both the expressions must be same and the constant in both the expressions must be same.
Simplify the left expression and equate the coefficients and constants.
3(2x + c) = 6x + 2 + c --> 6x + 3c = 6x + 2 + c.
Coefficients: The coefficients are same on both sides.
Constants:
Left expression constant is 3c.
Right expression constant is 2 + c.
Equate and determine the value of c that makes both sides equal. We can see that if c is 1, then constant on both the sides will equal to 3. Hence, c = 1. See calculation below.
3c = 2 + c --> 3c - c = 2 --> 2c = 2 --> c = 1.
Updated: Jul 11, 2021
bx + 8y = c
5x + 8y = 2c
In the system of equations above, for which of the following values of b does the system have no solution, where b and c are constants?
A) 1
B) 3
C) 4
D) 5
Maps to Category 9 of the book.
There is a flashcard for this concept accessible from the Resources page.
Answer posted on 07/11/2021: Correct answer choice is D.
Detailed Solution
Solution without calculation: This question can also be solved without any calculation. See logic below.
In both the equations, the coefficient of b is same. For the system to have no solution, the coefficient of a must also be same in both the equations. Hence, the coefficient of a must be 5 in both the equations.