#### Answer

Brian needs $8\frac{1}{3}$ cups of tomato sauce to make $2\frac{1}{2}$ times the usual amount of spaghetti sauce.

#### Work Step by Step

Let $x$ = the number of cups of tomato sauce Brian needs
Brian use $3\frac{1}{3}$ cups of tomato sauce for 1 spaghetti sauce recipe.
Brian needs to use $x$ cups of tomato sauce for $2\frac{1}{2}$ times the usual amount of his spaghetti sauce recipe.
Ratio and proportion can be used to solve this problem.
Setting up the ratio and proportion gives
$$\dfrac{3\frac{1}{3}}{1} = \dfrac{x}{2\frac{1}{2}}$$
Converting the mixed numbers to improper fractions give:
$$\dfrac{\frac{10}{3}}{1}=\dfrac{x}{\frac{5}{2}}$$
Cross-multiply to obtain:
$$1(x) = \frac{10}{3} \cdot \frac{5}{2}
x=\frac{50}{6}
\\x=8\frac{2}{6}
\\x=8\frac{1}{3}$$
Thus, Brian needs $8\frac{1}{3}$ cups of tomato sauce to make $2\frac{1}{2}$ times the usual amount of spaghetti sauce.