An arithmetic sequence is a sequence of numbers a1, a2, a3,... where an - an-1 is the same value for all n. For example 2, 4, 6, 8, 10,....is such a sequence where the difference between adjoining numbers is 2. Given a, b, c, d and e are consecutive members of such a sequence, and that a + b + c + d + e = 75, what is the value of c?
Chloe is setting up a factory to manufacture files. If she buys a machine that costs $52690, then she can manufacture a file for $4. On the other hand, if she buys a machine that costs $47100, she can manufacture a file for $5.3. How many file should she manufacture, so that total cost is the same no matter which machine she buys?
Tony wants to print some brochures for his business. If he goes for one style, it will cost him $103 plus $0.2 per brochure. If he goes for the other style, it will cost him $10 plus $0.5 per brochure. For how many brochures will the price for both styles be the same?
Leoni transfers mangoes from one larger box to smaller boxes. When the larger box is emptied, mangoes fill 5 smaller boxes and still 8 mangoes remained outside. If the number of mangoes in each smaller box is y, what was the number of mangoes in the larger box?