a. The equation we get is <u>10(1.5 + x) = 80</u>, where x is the number of hours Sheila can afford to hire the babysitter.
b. Sheila can afford the babysitter for <u>6 hours and 30 minutes</u>.
c. The equation we get is <u>15(1 + x) = 80</u>, where x is the number of hours Sheila can afford to hire the new babysitter.
d. Sheila can afford to hire the new babysitter for <u>4 hours and 20 minutes</u>, while the first babysitter was hired for <u>6 hours and 30 minutes</u>.
Thus, Sheila <u>can't afford</u> the same amount of babysitting from the second sitter as she could from the first sitter.
a. We assume the hours affordable to Sheila be x hours.
Per hour charge of the babysitter = $10.
Time taken by the babysitter traveling = 1.5 hours.
Therefore, total chargeable time = 1.5 + x.
Therefore, the total charge by the babysitter = $10(1.5 + x).
This needs to be equal to the amount Sheila is willing to spend, that is, $80.
Thus, the equation we get is: 10(1.5 + x) = 80.
b. We are asked to determine the hours Sheila can afford to hire the babysitter.
We have got the equation 10(1.5 + x) = 80, where x is the hours Sheila can afford to hire the babysitter.
Thus, by solving this equation, we can determine the hours Sheila can afford to hire the babysitter.
10(1.5 + x) = 80,
or, 1.5 + x = 8,
or, x = 8 - 1.5 = 6.5 = 6 hours and 30 minutes.
Thus, Sheila can afford the babysitter for 6 hours and 30 minutes.
c. Per hour charge of the new babysitter = $15.
Time taken by the new babysitter traveling = 1 hour.
Therefore, total chargeable time = 1 + x.
Therefore, the total charge by the new babysitter = $15(1 + x).
This needs to be equal to the amount Sheila is willing to spend, that is, $80.
Thus, the equation we get is: 15(1 + x) = 80.
d. We are asked whether Sheila affords the same amount of babysitting from the second sitter as she could from the first sitter.
To determine this, we need to find the hours she affords from the second babysitter, for which, we solve the equation 15(1 + x) = 80 as follows:
15(1 + x) = 80,
or, 1 + x = 80/15,
or, x = 80/15 - 1 = 65/15 = 13/3 = 4 hours and 20 minutes.
Sheila can afford to hire the new babysitter for 4 hours and 20 minutes, while the first babysitter was hired for 6 hours and 30 minutes.
Thus, Sheila can't afford the same amount of babysitting from the second sitter as she could from the first sitter.
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