Translating words into extra equations can help solve material balance problems. Write an expression for an extra equation for each of the following problem statements.

$($a$)$

Madeleine and Ferdinand wanted to enjoy a cold drink on a hot summer day. The pitcher held $1\mathrm{.}5$ L of the drink. They mixed $65$ wt$\%$ iced tea with the balance lemonade.

$($b$)$

The molar flow rate of cold water is four times larger than that of the hot water that enters a mixer.

$($c$)$

The ratio of the mole fraction of benzene $($B$)$ to the mole fraction of toluene $($T$)$ is the same in Streams $5$ and $6.$

$($d$)$

A filter removes $94\%$ of the solids entering.