The equation y = 12x describes the amount of money Louis earns, where x is the number of hours he works and y is the amount of money he earns. The table shows the amount of money Carl earns for different numbers of hours worked. Carl’s Earnings Time (h) 3 5 8 10 Money earned ($) 45 75 120 150 (a) How much money does Carl earn per hour? Show your work. (b) Who earns more per hour? Justify your answer. (c) Draw a graph that represents Carl’s earnings over time in hours. Remember to label the axes.
need help please.
from your given data:
3(15) = 45
5(15) = 75
...
10(15) = 150
looka like Carl makes $15 per hour
and Louis' rate is $12 per hour
take over
can you please show me how to do the graph? I'm lost there.
(a) To find how much money Carl earns per hour, we can divide the money earned by the number of hours worked.
For the first row, when Carl works for 3 hours, he earns $45. So, his earnings per hour would be:
$45 ÷ 3 = $15 per hour
For the second row, when Carl works for 5 hours, he earns $75. So, his earnings per hour would be:
$75 ÷ 5 = $15 per hour
For the third row, when Carl works for 8 hours, he earns $120. So, his earnings per hour would be:
$120 ÷ 8 = $15 per hour
For the last row, when Carl works for 10 hours, he earns $150. So, his earnings per hour would be:
$150 ÷ 10 = $15 per hour
Therefore, Carl earns $15 per hour.
(b) To determine who earns more per hour, we need to compare Carl's earnings per hour ($15) with Louis' earnings per hour. However, we don't have any information about Louis' earnings per hour given in the question. Without this information, we cannot determine who earns more per hour.
(c) To draw a graph representing Carl's earnings over time in hours, we need to plot the points from the given table on a graph.
The x-axis (horizontal) represents Time (in hours), and the y-axis (vertical) represents Money earned (in dollars).
The points on the graph would be:
(3, 45)
(5, 75)
(8, 120)
(10, 150)
After plotting these points, we can connect them with a line to represent Carl's earnings over time.
(a) To find the amount of money Carl earns per hour, we need to divide the money earned by the number of hours worked.
For Carl:
3 hours = $45
5 hours = $75
8 hours = $120
10 hours = $150
To find the money earned per hour, we divide the money earned by the number of hours worked:
Money earned per hour = Money earned / Number of hours
For 3 hours: Money earned per hour = $45 / 3 = $15/hour
For 5 hours: Money earned per hour = $75 / 5 = $15/hour
For 8 hours: Money earned per hour = $120 / 8 = $15/hour
For 10 hours: Money earned per hour = $150 / 10 = $15/hour
Therefore, Carl earns $15 per hour.
(b) To compare who earns more per hour, we need to compare the money earned per hour for both Louis and Carl.
For Louis, the equation y = 12x represents the amount of money he earns per hour. We can use this equation to find Louis' earnings per hour for any given number of hours worked.
For example, if Louis works 5 hours,
Money earned by Louis = 12 * 5 = $60
Comparing $15 per hour earned by Carl with $60 earned by Louis in the same time (5 hours), we can see that Louis earns more per hour than Carl.
Justification: The equation y = 12x shows that for every hour worked, Louis earns 12 times the amount of money. In this case, Louis earns $60 for 5 hours worked, which is greater than the $15 earned by Carl for the same amount of time.
Therefore, Louis earns more per hour than Carl.
(c) To draw a graph that represents Carl's earnings over time in hours, we will use the given data in the table.
On the x-axis, we will represent the time in hours and on the y-axis, we will represent the amount of money earned.
Plot the points (3, 45), (5, 75), (8, 120), and (10, 150) on the graph and connect them with straight lines.
The graph will start at (3, 45) and end at (10, 150), with the line gradually increasing.
Label the x-axis as "Time (h)" and the y-axis as "Money earned ($)".
This graph represents the relationship between the time spent working and the money earned by Carl.