Which table represents viable solutions for [tex]y=5x[/tex], where [tex]x[/tex] is the number of tickets sold for the school play and [tex]y[/tex] is the amount of money collected for the tickets?
School Play Tickets
Tickets ([tex]x[/tex])
Money Collected ([tex]y[/tex])
-100
-500
-8
-125
40
250
600
1000
School Play Tickets
Tickets ([tex]x[/tex])
Money Collected ([tex]y[/tex])
-20
-100
20
100
100
500
100
545
School Play Tickets
Tickets ([tex]x[/tex])
Money Collected ([tex]y[/tex])
0
0
10
50
51
255
400
2000
School Play Tickets
Tickets ([tex]x[/tex])
Money Collected ([tex]y[/tex])
5
8
85
150
80
400
Answer (2)
Check each table to see if the equation y = 5 x holds for all pairs of ( x , y ) .
In Table 1, 5 ( − 8 ) = − 40 , but the table shows -125, so it's incorrect.
In Table 2, 5 ( 100 ) = 500 , but the table shows 545, so it's incorrect.
In Table 3, all pairs satisfy y = 5 x .
Therefore, Table 3 represents viable solutions: T ab l e 3 .
Explanation
Problem Analysis We are given the equation y = 5 x , where x represents the number of tickets sold for a school play and y represents the amount of money collected. We need to determine which of the provided tables contains only pairs of ( x , y ) values that satisfy this equation. We will check each table individually.
Checking Table 1 Table 1:
For x = − 100 , y = 5 ( − 100 ) = − 500 . This matches the table.
For x = − 8 , y = 5 ( − 8 ) = − 40 . The table shows y = − 125 , which does not match. Since not all pairs satisfy the equation, Table 1 is not the correct table.
Checking Table 2 Table 2:
For x = − 20 , y = 5 ( − 20 ) = − 100 . This matches the table.
For x = 20 , y = 5 ( 20 ) = 100 . This matches the table.
For x = 100 , y = 5 ( 100 ) = 500 . This matches the table.
For x = 100 , y = 5 ( 100 ) = 500 . The table shows y = 545 , which does not match. Since not all pairs satisfy the equation, Table 2 is not the correct table.
Checking Table 3 Table 3:
For x = 0 , y = 5 ( 0 ) = 0 . This matches the table.
For x = 10 , y = 5 ( 10 ) = 50 . This matches the table.
For x = 51 , y = 5 ( 51 ) = 255 . This matches the table.
For x = 400 , y = 5 ( 400 ) = 2000 . This matches the table. All pairs in Table 3 satisfy the equation.
Checking Table 4 Table 4:
For x = 5 , y = 5 ( 5 ) = 25 . The table shows y = 8 , which does not match. Since not all pairs satisfy the equation, Table 4 is not the correct table.
Final Answer Therefore, the table that represents viable solutions for y = 5 x is Table 3.
Examples
Understanding linear relationships like y = 5 x is crucial in everyday scenarios. For instance, if you're saving money at a constant rate, say 5 p er d a y , t h ee q u a t i o nh e lp syo u p re d i c t yo u r t o t a l s a v in g s ( y ) ba se d o n t h e n u mb ero fd a ys ( x$). This principle applies to budgeting, calculating travel distances at a constant speed, or even estimating the cost of buying multiple items at a fixed price. Recognizing and applying such relationships simplifies planning and decision-making in various real-life situations.
The viable solutions for the equation y = 5 x can be found in Table 3, as all pairs of ( x , y ) values satisfy the equation. Tables 1, 2, and 4 do not contain all matching pairs. Therefore, the correct answer is Table 3.
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