HELP twice a number plus twice a second number is 310. The difference between the numbers is 55. Find the numbers by writing and solving a system of equations. Explain how you solved the system. PLEASE HELP ME Thank you! I got numbers are 182.5 and 127.5 but I don't understand how to set up the system equations
Answers
The numbers by writing and solving a system of equations are 50 and 105
System of equations
Let the unknown numbers be x and y
If twice a number plus twice a second number is 310, then;
2x + 2y = 310
x + y = 155
x = 155 - y
Also, If the difference of the numbers is 55, hence;
x - y = 55
155 - y - y = 55
155 - 2y = 55
-2y = 55 - 505
2y = 100
y = 50
Substitute y = 25 into 1 to have:
x = 155 - 50
x = 105
Hence the numbers by writing and solving a system of equations are 50 and 105
Learn more on system of equations here: brainly.com/question/847634
The difference between the numbers is 55.
Divide the first equation by 2 to get a 3rd equation:
Add the second and third equations together:
Put x=105 into the second equation to get:
So you're answers are x=105 and y=50.
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The correct interpretation is that the slope of the line is indeed 15, indicating that the cost of one admission ticket is $15, and point (1, 15) represents the unit rate.
The correct answer is option B.
The given graph illustrates the relationship between the number of people in a group and the cost of admission tickets. The statement correctly identifies that the slope of the line on this graph represents the unit rate of admission tickets.
The slope of a line on a graph signifies the rate of change between the two variables involved. In this context, the horizontal axis (x-axis) represents the number of people in a group, while the vertical axis (y-axis) represents the cost of admission tickets.
To compute the slope, you select two points on the line. The statement correctly utilizes the points (0, 0) and (1, 15) for this purpose. The slope formula, which is the change in y divided by the change in x, is applied as follows:
Slope = (y2 - y1) / (x2 - x1)
In this instance, x1 = 0, y1 = 0, x2 = 1, and y2 = 15. Substituting these values into the formula yields:
Slope = (15 - 0) / (1 - 0) = 15 / 1 = 15
This signifies that for each additional person in the group, the cost of admission tickets increases by $15. Consequently, $15 represents the cost of one admission ticket, and the point (1, 15) represents the unit rate.
Therefore, the conclusion that option B is the answer is accurate.
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The question probable may be:
The graph below shows the relationship between the number of people in a group and the total cost of admission tickets for a circus