mrsmarthi wrote:
For each landscaping job that takes more than 4 hours, a certain contractor charges a total of r dollars for the first 4 hours plus 0.2*r dollars for each additional hour or fraction of an hour where r > 100, Did a particular landscaping job took more than 10 hours.
(1) The contractor charges a total of $288 for the job.
(2) The contractor charges a total of 2.4r dollars for the job.
Is t > 10?
Statement 1:
Test whether it's possible that t=10.
Case 1: t = 10 hours
Since $r dollars is charged for the first 4 hours and $0.2r is charged for each of the 6 additional hours, we get:
r + 0.2r(6) = 288
2.2r = 288
\(r = \frac{288}{2.2}\) ≈ 130
In this case, t=10. so the answer to the question stem is NO.
Test whether it's possible that t>10.
Case 2: t = 11 hours
Since $r dollars is charged for the first 4 hours and $0.2r is charged for each of the 7 additional hours, we get:
r + 0.2r(7) = 288
2.4r = 288\(r = \frac{288}{2.4} = 120\)
In this case, t>10, so the answer to the question stem is YES.
Since the answer is NO in Case 1 but YES in Case 2, INSUFFICIENT.
Statement 2:
The blue equation in Case 2 indicates that the total charge = 2.4r when t=11.
Thus, the answer to the question stem is YES.
SUFFICIENT.
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