For each of the following problems, set up an equation and solve.
(a) A company laid off one-sixth of its workforce because of falling sales. If the number of employees after the layoff is 690, how many employees were laid off?
(b) The current average property value is two-sevenths more than last year’s average value. What was last year’s average property value if the current average is $81 450?
(c) The total amount paid for a banquet, including gratuities of one-twentieth of the price quoted for the banquet, was $2457. How much of the amount paid were gratuities?
(d) A piece of property with a commercial building is acquired by H & A Investments for $184 000. If the land is valued at $2000 less than one-third the value of the building, how much of the amount paid should be assigned to land?
(e) The total average monthly cost of heat, power, and water for Sheridan Service for last year was $2010. If this year’s average is expected to increase by one-tenth over last year’s aver- age, and heat is $22 more than three-quarters the cost of power while water is $11 less than one-third the cost of power, how much should be budgeted on average for each month for each item?
(f) Remi Swimming Pools has a promotional budget of $87 500. The budget is to be allocated to direct selling, TV advertising, and newspaper advertising; according to a formula. The formula requires that the amount spent on TV advertising be $1000 more than three times the amount spent on newspaper advertising, and that the amount spent on direct selling be three-fourths of the total spent on TV advertising and news- paper advertising combined. How much of the budget should be allocated to direct selling?
(g) A product requires processing on three machines. Processing time on Machine A is three minutes less than four-fifths of the number of minutes on Machine B, and processing time on Machine C is five-sixths of the time needed on Machines A and B together. How many minutes of processing time is required on Machine C if the total processing time on all three machines is 77 minutes?
(h) Sport Alive sold 72 pairs of ski poles. Superlight poles sell at $30 per pair, while ordinary poles sell at $16 per pair. If the total sales value was $1530, how many pairs of each type were sold?
(i) A cash box contains $107 made up of quarters, one-dollar coins, and two-dollar coins. How many quarters are in the box if the number of one-dollar coins is one more than three-fifths of the number of two-dollar coins, and the number of quarters is four times the number of one-dollar coins and two-dollar coins together?