The problem says "3 1/2 cups of sugar took one cup of chocolate chips"
The ratio is: 3 1/2 sugar for each cup of chocolate.
We want to find the quantity of chocolate chips for "one and three-quarter cups of sugar"
First, let's convert 3 1/2 into an improper fraction:
[tex]3\frac{1}{2}=3+\frac{1}{2}=\frac{3\cdot2}{1\cdot2}+\frac{1}{2}=\frac{6}{2}+\frac{1}{2}=\frac{7}{2}[/tex]Now, we want to find an expression for "one and three-quarter". We can write:
[tex]1\frac{3}{4}=1+\frac{3}{4}=\frac{4}{4}+\frac{3}{4}=\frac{7}{4}[/tex]And now, we can use cross multiplication. If 7/2 of sugar needs 1 cup of chocolate, how many of chocolate if 7/4 of sugar is used? If we call x to the quantity of chocolate needed, we can wirte:
[tex]\frac{\frac{7}{2}}{\frac{7}{4}}=\frac{1}{x}[/tex]Now take the reciprocal on both sides:
[tex]\frac{\frac{7}{4}}{\frac{7}{2}}=x[/tex]And solve:
[tex]x=\frac{7}{4}\cdot\frac{2}{7}=\frac{2}{4}=\frac{1}{2}[/tex]Thus, the answer is: According to the recipe, the quantity of chocolate needed is 1/2 cup.
