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A bank efficiency ratio is the ratio of a bank's expenses to its revenue, expressed as a percentage. If a bank has
$222 million dollars in expenses and an efficiency ratio of
75%, what is its revenue in millions of dollars?

A bank efficiency ratio is the ratio of a bank's expenses to its revenue, expressed as a percentage. If a bank has $\$ 222$ million dollars in expenses and an efficiency ratio of $75 \%$ , what is its revenue in millions of dollars?

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Write linear functions: word problems

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Q. A bank efficiency ratio is the ratio of a bank's expenses to its revenue, expressed as a percentage. If a bank has

\$ 222

million dollars in expenses and an efficiency ratio of

75 \%

, what is its revenue in millions of dollars?

Define Efficiency Ratio: Let's denote the bank's revenue as $R$ (in millions of dollars). The efficiency ratio is the ratio of the bank's expenses to its revenue, expressed as a percentage. Given the efficiency ratio is $75\%$ , we can write the following equation: $\newline$ Efficiency Ratio = $(\text{Expenses} / \text{Revenue}) \times 100\%$ $\newline$ $75\% = (222 / R) \times 100\%$
Solve for Revenue: To find the revenue $R$ , we need to solve the equation for $R$ . First, we convert the percentage to a decimal by dividing by $100$ : $75\% = \frac{75}{100} = 0.75$ Now the equation becomes: $0.75 = \frac{222}{R}$
Convert Percentage to Decimal: Next, we multiply both sides of the equation by $R$ to get rid of the denominator: $\newline$ $0.75 \times R = 222$
Eliminate Denominator: Now, we divide both sides of the equation by $0.75$ to isolate $R$ : $\newline$ $R = \frac{222}{0.75}$
Isolate Revenue: Perform the division to find the value of $R$ : $R = 296$
Calculate Revenue: The bank's revenue is therefore $\$296$ million.

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