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Just for walking in the door, before any lessons,
Celeste . . . $5.00
Dora. . . . . $10.25
For 'H' hours of instruction,
Celeste . . . $7.25 x H
Dora . . . . . $6.50 x H .
Total cost to take lessons from
Celeste . . . 5 + 7.25H
Dora . . . . . 10.25 + 6.5 H
What is the number of hours ' H ' when both of their total costs
would be the same ?
5 + 7.25H = 10.25 + 6.5H
Subtract 6.5H from each side: 5 + 0.75H = 10.25
Subtract 5 from each side: 0.75H = 5.25
Divide each side by 0.75 : H = 5.25/0.75 = 7 hours
After 7 hours of instruction, Celeste's student and Dora's student
have both paid $55.75 . After that, Celeste's student pays 75¢
more for each hour of instruction than Dora's student pays.
Celeste . . . $5.00
Dora. . . . . $10.25
For 'H' hours of instruction,
Celeste . . . $7.25 x H
Dora . . . . . $6.50 x H .
Total cost to take lessons from
Celeste . . . 5 + 7.25H
Dora . . . . . 10.25 + 6.5 H
What is the number of hours ' H ' when both of their total costs
would be the same ?
5 + 7.25H = 10.25 + 6.5H
Subtract 6.5H from each side: 5 + 0.75H = 10.25
Subtract 5 from each side: 0.75H = 5.25
Divide each side by 0.75 : H = 5.25/0.75 = 7 hours
After 7 hours of instruction, Celeste's student and Dora's student
have both paid $55.75 . After that, Celeste's student pays 75¢
more for each hour of instruction than Dora's student pays.
In 7 hours of instruction will the cost is 55.75 for each instructor be the same.
Given that,
Celeste and Dora both offer guitar lessons.
Celeste charges an initial fee of $5.00, and an hourly rate of $7.25.
Dora has an initial fee of $10.25 and an hourly rate of $6.50.
We have to determine,
At how many hours of instruction will the cost for each instructor be the same?
According to the question,
Let t be the number of hours of instruction will the cost for each instructor be the same.
Celeste charges an initial fee of $5.00, and an hourly rate of $7.25.
[tex]\rm= 5 +7.25t[/tex]
Dora has an initial fee of $10.25 and an hourly rate of $6.50.
[tex]\rm = 10.25+6.50t[/tex]
Therefore,
On comparing the equation the value of the time t is,
[tex]\rm5+7.25t = 10.25+6.50t\\\\7.25t-6.50t = 10.25-5\\\\0.75t= 5.25\\\\t = \dfrac{5.25}{0.75}\\\\t = 7 \ hours[/tex]
Substitute the value of t in equation 1,
[tex]\rm= 5 +7.25t\\\\= 5+7.25(7)\\\\= 5+50.75\\\\= 55.75[/tex]
Hence, In 7 hours of instruction will the cost is 55.75 for each instructor to be the same.
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