1. During one month, a homeowner used600unitsof electricity and100 unitsof gas for a total cost of$360. The next month,400unitsof electricity and250unitsof gas were used for a total cost of$284. Find the cost per unit of gas.
2. A merchant mixed12lbof a cinnamon tea with3lbof spice tea. The15-poundmixture cost$24. A second mixture included14lbof the cinnamon tea and6lbof the spice tea. The20-poundmixture cost$33. Find the cost per pound of the cinnamon tea and of the spice tea.
3. A carpenter purchased60ft of redwood and90ft of pine for a total cost of$291. A second purchase, at the same prices, included90ftof redwood and60ftof pine for a total cost of$354. Find the cost per foot of redwood and of pine. Redwood_____ Pine_____
4. A company manufactures both mountain bikes and trail bikes. The cost of materials for a mountain bike is$60, and the cost of materials for a trail bike is$40. The cost of labor to manufacture a mountain bike is$90, and the cost of labor to manufacture a trail bike is$30. During a week in which the company has budgeted$1,700for materials and$1,950for labor, how many mountain bikes does the company plan to manufacture?
5. A baker purchased15lb of wheat flour and10lb of rye flour for a total cost of$20.25. A second purchase, at the same prices, included14lb of wheat flour and12lb of rye flour. The cost of the second purchase was$20.90. Find the cost per pound of the wheat flour and of the rye flour.
6. In a pen of goats and chickens, there are55heads and180feet. How many goats and chickens are in the pen? Goats__ Chickens___
7. A state employees' pension fund invested a total of one million dollars in two accounts that earned 3.5% and 4.5% annual simple interest. At the end of the year, the total interest earned from the two investments was$43,000. How much was invested at each rate?