answer:If the lens costs 300 and there is a 20% discount, then Mark will save 300 * 20% = 60 So the lens with the discount will cost 300 - 60 = 240 If Mark chooses the 220 lens instead, he will save 240 - 220 = 20 Therefore, Mark saves 20 by opting for the cheaper lens. 20 The answer is: 20

answer:We notice that begin{align*} frac{F_k}{F_{k - 1}} - frac{F_k}{F_{k + 1}} &= frac{F_k F_{k + 1} - F_k F_{k - 1}}{F_{k - 1} F_{k + 1}} &= frac{F_k (F_{k + 1} - F_{k - 1})}{F_{k - 1} F_{k + 1}} &= frac{F_k^2}{F_{k - 1} F_{k + 1}}. end{align*}Thus, [prod_{k = 2}^{100} left( frac{F_k}{F_{k - 1}} - frac{F_k}{F_{k + 1}} right) = prod_{k = 2}^{100} frac{F_k^2}{F_{k - 1} F_{k + 1}}.]The product telescopes, so [prod_{k = 2}^{100} frac{F_k^2}{F_{k - 1} F_{k + 1}} = frac{F_2^2}{F_1 F_3} cdot frac{F_3^2}{F_2 F_4} cdot frac{F_4^2}{F_3 F_5} dotsm frac{F_{100}^2}{F_{99} F_{101}} = frac{F_{100}^2}{F_1 F_{101}} = frac{F_{100}}{F_{101}}.]Therefore, (a,b) = boxed{(100,101)}.The answer is: (100,101)

answer:Christine earns a 12% commission on all the items she sells, so her commission for this month is 12% of 24000, which is 12/100 * 24000 = 2880. Out of her earnings, she allocates 60% to her personal needs, so she keeps 60/100 * 2880 = 1728 for herself. The remaining amount is what she saves, which is 2880 - 1728 = 1152. Therefore, Christine saved 1152 this month. 1152 The answer is: 1152

answer:James bought 5 packs of beef, each weighing 4 pounds, so he bought a total of 5 * 4 = 20 pounds of beef. The price of beef is 5.50 per pound, so the total amount James paid is 20 * 5.50 = 110. 110 The answer is: 110