Miscate owns Cool Groove, a company that sells and installs automobile sound systems. Cool Grove charges $185 for each small system and $235 for each large system installed. Harroda reported that last month her company installed 135 systems and collected $27.225 in total receipts. During that month, how many small systems and how many large systems were installed?

1. One way to work mixture problems like this is to consider the effect of all sales being for the smaller amount. In that case, revenue would be 135*$185 = $24,975. That is $2250 less than actual revenue. For each large system sold instead of a small one, there is $50 in additional revenue. The $2250 in additional revenue requires that 2250/50 = 45 large systems be sold.

2. We know that Rafael's overtime pay is $912.60 - 40*$14.40 = 336.60. None of the offered answers computes to the correct pay amount.  

If you made a typo and the correct total pay is $921.60, then an overtime rate of 1.5 times base pay will require 16 hours of overtime; an overtime rate of 3 times base pay will only require 8 hours of overtime. Overtime hours = $921.60/$14.40 = 64 equivalent hours. Subtracting 40 hours of straight time, the resulting product of hours and multiplier will be 64 - 40 = 24. That is it could be 16 hours at 1.5 times, or 8 hours at 3 times.

3. One of the problems here is to figure the number of hours in a month. If you consider there to be 4 1/3 weeks in a month, Robin needs to work $3280/(13/3)/14.90 = 50.80 equivalent hours. The 10.80 equivalent overtime hours will be 10.80/1.5 = 7.20 clock hours, closest to 7.25 among the answers. (Other choices for weeks/hours in a month give answers that match none of those offered.)

4. $750/$19.50 = 38.46, closest to 38.50 among the answers offered.

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