Mathematics, 17.07.2019 05:30 memo1102

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. at how many hours of instruction will the cost for each instructor be the same?

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Answer from: kaleb6816

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.

$\rm= 5 +7.25t$

Dora has an initial fee of $10.25 and an hourly rate of $6.50.

$\rm = 10.25+6.50t$

Therefore,

On comparing the equation the value of the time t is,

$\rm5+7.25t = 10.25+6.50t\\\\7.25t-6.50t = 10.25-5\\\\0.75t= 5.25\\\\t = \dfrac{5.25}{0.75}\\\\t = 7 \ hours$

Substitute the value of t in equation 1,

$\rm= 5 +7.25t\\\\= 5+7.25(7)\\\\= 5+50.75\\\\= 55.75$

Hence, In 7 hours of instruction will the cost is 55.75 for each instructor to be the same.

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Answer from: GoAheadAndSmileToday

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.

Answer from: Quest

step-by-step explanation:

Answer from: Quest

so, converting firstly the mixed fractions to improper fractions and then "adding".

$\bf \stackrel{mixed}{2\frac{9}{10}}\implies \cfrac{2\cdot 10+9}{10}\implies \stackrel{improper}{\cfrac{29}{10}}~\hfill \stackrel{mixed}{5\frac{4}{15}}\implies \cfrac{5\cdot 15+4}{15}\implies \stackrel{improper}{\cfrac{79}{15}} [-0.35em] ~\dotfill$

$\bf -\cfrac{29}{10}+\left( -\cfrac{79}{15} \right)\implies -\cfrac{29}{10}-\cfrac{79}{15}\implies \stackrel{\textit{using the lcd of 30}}{\cfrac{-(3)29-(2)79}{30}}\implies \cfrac{-87-158}{30} \cfrac{-245}{30}\implies -\cfrac{49}{6}\implies -8\frac{1}{6}$

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