Questions: (a) Compute the ratio of Total Charges (Tuition and Fees and Room and Board) for Public Four-Year In-State from 2020-21 to 2021-22 and scale the second quantity to 1. The scaled ratio is 0.981: 1.000 (Type integers or decimals rounded to three decimal places as needed.) (b) Fill in the following ratio table for 2021-22, using the values given in the second row of the table to avoid round-off error whenever possible. Private Room and Board Public Four-Year Room and Board In-State Public Two-Year Room and Board In-State 13,594 11,881 9,316 1 100 (Do not include the symbol in your answer. Do not round until the final answer. Then round to two decimal places as needed.)

(a) Compute the ratio of Total Charges (Tuition and Fees and Room and Board) for Public Four-Year In-State from 2020-21 to 2021-22 and scale the second quantity to 1.

The scaled ratio is 0.981: 1.000
(Type integers or decimals rounded to three decimal places as needed.)
(b) Fill in the following ratio table for 2021-22, using the values given in the second row of the table to avoid round-off error whenever possible.
Private Room and Board  Public Four-Year Room and Board In-State  Public Two-Year Room and Board In-State
13,594  11,881  9,316
  1  
100    
(Do not include the  symbol in your answer. Do not round until the final answer. Then round to two decimal places as needed.)
Transcript text: (a) Compute the ratio of Total Charges (Tuition and Fees and Room and Board) for Public Four-Year In-State from 2020-21 to 2021-22 and scale the second quantity to 1. The scaled ratio is $0.981: 1.000$ (Type integers or decimals rounded to three decimal places as needed.) (b) Fill in the following ratio table for 2021-22, using the values given in the second row of the table to avoid round-off error whenever possible. \begin{tabular}{|c|c|c|} \hline \begin{tabular}{c} Private Room \\ and Board \end{tabular} & \begin{tabular}{c} Public Four-Year \\ Room and Board \\ In-State \end{tabular} & \begin{tabular}{c} Public Two-Year \\ Room and Board \\ In-State \end{tabular} \\ \hline$\$ 13,594$ & $\$ 11,881$ & $\$ 9,316$ \\ \hline$\square$ & 1 & $\square$ \\ \hline 100 & $\square$ & $\square$ \\ \hline \end{tabular} (Do not include the $\$$ symbol in your answer. Do not round until the final answer. Then round to two decimal places as needed.)
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Solution

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Solution Steps

(a) To compute the ratio of Total Charges for Public Four-Year In-State from 2020-21 to 2021-22, we need to divide the Total Charges for 2020-21 by the Total Charges for 2021-22. Then, we scale the second quantity (2021-22) to 1.

(b) To fill in the ratio table, we need to calculate the ratios of the given values and then use these ratios to fill in the missing values. Specifically, we will use the given values to find the ratios and then scale them appropriately.

Step 1: Compute the Ratio of Total Charges for Public Four-Year In-State from 2020-21 to 2021-22

Given:

  • Total Charges for 2020-21: \(0.981\)
  • Total Charges for 2021-22: \(1.000\)

The ratio is already given as \(0.981:1.000\).

Step 2: Calculate the Ratios for the Ratio Table

Given:

  • Private Room and Board: \( \$13,594 \)
  • Public Four-Year Room and Board In-State: \( \$11,881 \)
  • Public Two-Year Room and Board In-State: \( \$9,316 \)

Calculate the ratios: \[ \text{Ratio of Private to Public Four-Year} = \frac{13594}{11881} \approx 1.1442 \] \[ \text{Ratio of Public Two-Year to Public Four-Year} = \frac{9316}{11881} \approx 0.7841 \]

Step 3: Fill in the Ratio Table

Using the calculated ratios:

  • Private Room and Board scaled to Public Four-Year Room and Board In-State: \[ 1.1442 \]
  • Public Two-Year Room and Board scaled to Public Four-Year Room and Board In-State: \[ 0.7841 \]

For the 100 scaled values:

  • Private Room and Board (100 scaled): \[ 100 \times 1.1442 = 114.42 \]
  • Public Two-Year Room and Board (100 scaled): \[ 100 \times 0.7841 = 78.41 \]

Final Answer

(a) The ratio of Total Charges for Public Four-Year In-State from 2020-21 to 2021-22 is: \[ \boxed{0.981:1.000} \]

(b) The filled ratio table for 2021-22 is: \[ \begin{array}{|c|c|c|} \hline \text{Private Room and Board} & \text{Public Four-Year Room and Board In-State} & \text{Public Two-Year Room and Board In-State} \\ \hline 13594 & 11881 & 9316 \\ \hline 1.1442 & 1 & 0.7841 \\ \hline 100 & 114.42 & 78.41 \\ \hline \end{array} \]

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