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Question 1151480: Smart student learning center charges students a registration fee of $25 plus an hourly rate of $30 for after school tutoring. Brilliant learning center charges students for after school tutoring based on the table below :
Brilliant student learning center
Hours of tutoring (x) Total cost (y)
1 $45
3 $115
5 $185
7 $255
If a student needs 4 hours of tutoring, which statement is true?
A. Smart student learning center charges$5 more than Brillant student learning center.
B.
Brilliant student learning center charges $5 more than Smart student learning center.
C.Smart student learning center charges #35 more than Brilliant student learning center.
D. Brillant student learning center charges $35 more than Smart student learning center.
Found 2 solutions by jim_thompson5910, greenestamps:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
x = number of hours of tutoring
y = total cost
Smart student center learning, which I'll just abbreviate to "Company S", charges a registration fee of $25 plus an hourly rate of $30. This means the equation for Company S is
y = 30x+25
Note how this equation is in the form y = mx+b
m = slope = 30
b = y intercept = 25
The slope tells us how much y goes up each time x increases by 1 (ie, for each increase of 1 hour, the cost goes up by $30)
The y intercept is the starting cost, or the cost if you have x = 0 hours of tutoring.
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I'll abbreviate "Brilliant learning center" as "Company B". This company has the following table of x,y values.
Pick two points from that table, say the first two rows
Row1: (x1,y1) = (1, 45)
Row2: (x2,y2) = (3, 115)
Compute the slope between those two points
m = (y2-y1)/(x2-x1)
m = (115-45)/(2)
m = 70/2
m = 35
The slope is 35, which means Company B charges $35 an hour.
Use any row of the table as the (x,y) value. I'll use row 1, so (x,y) = (1,45)
Plug those values, along with m = 35, into the form
y = mx+b
and solve for b
y = mx+b
45 = 35*1+b
45 = 35+b
45-35 = b
10 = b
b = 10
The starting cost for Company B is $10, i.e. this is the registration cost or the cost of having x = 0 hours of tutoring.
Overall the equation for Company B is
y = 35x+10
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To summarize so far:
y = 30x+25 is the cost equation for Company S
y = 35x+10 is the cost equation for Company B
From here we plug x = 4 into each equation and simplify using PEMDAS
Company S
y = 30*x+25
y = 30*4+25
y = 120+25
y = 145
Having x = 4 hours of tutoring at Company S will cost you y = 145 dollars.
Company B
y = 35*x+10
y = 35*4+10
y = 140+10
y = 150
Having x = 4 hours of tutoring at Company B will cost you y = 150 dollars.
We see the difference of the two companies is 150-145 = 5 dollars. So Company S is cheaper by $5. Or put another way, Company B is $5 more expensive.
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Final Answer:
B) Brilliant student learning center charges $5 more than Smart student learning center.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
To find the cost of 4 hours of tutoring at smart learning center, simply use the given information: $25 for registration plus 4 hours at $30 per hour means
$25+4($30) = $25+$120 = $145.
There are at least two ways to find the cost of 4 hours of tutoring at brilliant learning center that are easier and much faster than using the given data to find the registration fee and hourly cost.
You can reason that the cost of 4 hours is halfway between the cost for 3 hours and the cost for 5 hours: ($115+$185)/2 = $300/2 = $150.
Or you can use the given data to observe that the cost of tutoring is $70 for 2 hours and therefore $35 for 1 hour; then $115 for 3 hours plus one more hour at $35 per hour makes $115+$35 = $150.
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