A miniature golf course charges different prices for adults and children. On Saturday, 50 adults and 50 children played, and the golf course earned $800. On Sunday, 65 adults and 75 children played, and the golf course earned $1,100. How much does the golf course charge for adults?
A.
$6
B.
$8
C.
$10
D.
$16
Let's denote the price for adults as $A and the price for children as $C.
From the given information, we can set up a system of equations:
50A + 50C = 800
65A + 75C = 1100
Solving this system of equations, we can find the values for A and C.
Multiplying the first equation by 13, we get:
650A + 650C = 10400
65A + 75C = 1100
Subtracting the second equation from the first equation, we get:
585A = 9300
Dividing both sides by 585, we find:
A = 16
Therefore, the golf course charges $16 for adults, which is answer choice D.
The lesson length (in minutes) and the cost (in dollars) of piano lessons given by nine different piano instructors are shown in the table below.
The table shows 30 minutes lesson costs 45 dollars by the first instructor, 30 minutes lesson costs 25 dollars by the second instructor, 45 minutes lesson costs 60 dollars by the third instructor, 20 minutes lesson costs 35 dollars by the fourth instructor, 60 minutes lesson costs 50 dollars by the fifth instructor, 50 minutes lesson costs 55 dollars by the sixth instructor, 60 minutes lesson costs 75 dollars by the seventh instructor, 30 minutes lesson costs 50 dollars by the eighth instructor, and 60 minutes lesson costs 80 dollars by the ninth instructor.
Which of the following scatter plots correctly displays this data?
A.
A scatter plot on graph titled 'piano lessons' showing 'lesson length in minutes' from 0 to 80 along the x-axis and 'lesson cost in dollars' from 0 to 80 along the y-axis, is shown with 9 data points at (20, 25), (30, 35), (30, 45), (30, 50), (45, 50), (50, 55), (60, 60), (60, 75), and (60, 80).
B.
A scatter plot on graph titled 'piano lessons' showing 'lesson length in minutes' from 0 to 80 along the x-axis and 'lesson cost in dollars' from 0 to 80 along the y-axis, is shown with 9 data points at (20, 35), (25, 30), (30, 45), (30, 50), (45, 60), (50, 55), (60, 50), (60, 75), and (60, 80).
C.
A scatter plot on graph titled 'piano lessons' showing 'lesson length in minutes' from 0 to 80 along the x-axis and 'lesson cost in dollars' from 0 to 80 along the y-axis, is shown with 9 data points at (20, 35), (30, 25), (30, 45), (30, 50), (45, 60), (50, 55), (60, 50), (60, 75), and (60, 80).
D.
A scatter plot on graph titled 'piano lessons' showing 'lesson length in minutes' from 0 to 80 along the x-axis and 'lesson cost in dollars' from 0 to 80 along the y-axis, is shown with 9 data points at (25, 30), (35, 20), (45, 30), (50, 30), (50, 60), (55, 50), (60, 45), (75, 60), and (80, 60).
The scatter plot should have the lesson length (in minutes) on the x-axis and the lesson cost (in dollars) on the y-axis.
From the given information, we can organize the data into pairs of (lesson length, lesson cost):
(30, 45), (30, 25), (45, 60), (20, 35), (60, 50), (50, 55), (60, 75), (30, 50), (60, 80)
Looking at the answer choices:
A. (20, 25), (30, 35), (30, 45), (30, 50), (45, 50), (50, 55), (60, 60), (60, 75), (60, 80)
This answer choice incorrectly repeats the values of (30, 45) and (60, 60).
B. (20, 35), (25, 30), (30, 45), (30, 50), (45, 60), (50, 55), (60, 50), (60, 75), (60, 80)
This answer choice incorrectly lists (25, 30) instead of (30, 25).
C. (20, 35), (30, 25), (30, 45), (30, 50), (45, 60), (50, 55), (60, 50), (60, 75), (60, 80)
This answer choice correctly lists all the data points.
D. (25, 30), (35, 20), (45, 30), (50, 30), (50, 60), (55, 50), (60, 45), (75, 60), (80, 60)
This answer choice incorrectly lists (35, 20) instead of (20, 35) and (50, 30) instead of (30, 50).
Therefore, the correct scatter plot is in answer choice C.
Solve for x.
3x + 2 = x + 8
A.
1.5
B.
2.5
C.
3
D.
5
To solve for x, we need to isolate x on one side of the equation.
First, we can simplify the equation by combining like terms:
3x + 2 = x + 8
Next, we can subtract x from both sides of the equation to move the x term to one side:
2x + 2 = 8
Next, we can subtract 2 from both sides of the equation:
2x = 6
Finally, we can divide both sides of the equation by 2 to solve for x:
x = 3
Therefore, the solution for x is 3, which corresponds to answer choice C.