Question

Andy, who loves to cook, makes apple cobbler for his family. The recipe (serves 6) calls for 3 1/4 pounds of apples, 4 3/4 cups of flour,1/7 cup of margarine, 3 5/8 cups of sugar, and 2 teaspoons of cinnamon. Since guests are coming, Andy wants to make a cobbler that will serve 15 (or increase the recipe 2 1/2 times). How much of each ingredient should Andy use?

Answer 1

$\bf \stackrel{apples}{3\frac{1}{4}}\implies \cfrac{3\cdot 4+1}{4}\implies \boxed{\cfrac{13}{4}} \\\\\\ \stackrel{flour}{4\frac{3}{4}}\implies \cfrac{4\cdot 4+3}{4}\implies \boxed{\cfrac{19}{4}} \\\\\\ \stackrel{margarine}{\cfrac{1}{7}} \\\\\\ \stackrel{sugar~cups}{3\frac{5}{8}}\implies \cfrac{3\cdot 8+5}{8}\implies \boxed{\cfrac{29}{8}} \\\\\\ \stackrel{cinnamon~teaspoons}{2}$

now, how much is 2 and a half of each? well, is just the product of 2 and 1/2 times each.

$\bf 2\frac{1}{2}\implies\cfrac{2\cdot 2+1}{2}\implies \cfrac{5}{2}\qquad thus \\\\\\ \cfrac{5}{2}\left( \cfrac{13}{4} \right)\implies \cfrac{5\cdot 13}{2\cdot 4}\implies \cfrac{65}{8}\implies \stackrel{apples}{7\frac{9}{8}} \\\\\\ \cfrac{5}{2}\left( \cfrac{19}{4} \right)\implies \cfrac{5\cdot 19}{2\cdot 4}\implies \cfrac{95}{4}\implies \stackrel{flour}{23\frac{3}{4}}$

$\bf \cfrac{5}{2}\left( \cfrac{1}{7} \right)\implies \cfrac{5\cdot 1}{2\cdot 7}\implies \stackrel{margarine}{\cfrac{5}{14}} \\\\\\ \cfrac{5}{2}\left( \cfrac{29}{8} \right)\implies \cfrac{5\cdot 29}{2\cdot 8}\implies \cfrac{145}{16}\implies \stackrel{sugar~cups}{9\frac{1}{16}} \\\\\\ \cfrac{5}{2}(2)\implies \stackrel{cinnamon~teaspoons}{5}$