Question

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?​

Answer 1

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.