HW 2.1 Ratios and Proportions-Maria Huerta

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1/24/24, 4:07 PM HW 2.1 Ratios and Proportions-Maria Huerta https://tdx.acs.pearsonprd.tech/api/v1/print/highered 1/3 Student: Maria Huerta Date: 01/24/24 Instructor: Dania Sinibaldi Course: Quantitative Reasoning O06B SP24 Assignment: HW 2.1 Ratios and Proportions Use the tables to answer parts (a) and (b). (a) Compute the ratio of Total Charges for Public Four-Year In-State from 2013-14 to 2012-13 and scale the second quantity to 1. Click on the icon to view the table for part (a). 1 (b) Fill in the ratio table for 2013-14, using the values given in the second row of the table to avoid round-off error whenever possible. Click on the icon to view the table for part (b). 2 (a) Compute the ratio of Total Charges for Public Four-Year In-State from 2013-14 to 2012-13 and scale the second quantity to 1. First identify the necessary values from the table. To do this, identify the row of the table labeled "Public Four-Year In-State" and follow it to the right. The correct values are in the "Total Charges" section, in the columns labeled 2013-14 and 2012-13. The Total Charges for Public Four-Year In-State for 2013-14 are $ and the Total Charges for Public Four-Year In-State for 2012-13 are $ . 22,085 17,712 Set up the ratio of Total Charges for Public Four-Year In-State for 2013-14 to Total Charges for Public Four-Year In-State for 2012-13. The ratio is . 22,085 17,712 To scale the second, or bottom, quantity to 1, find an equivalent ratio to where the denominator is 1. 22,085 17,712 To do this, set the ratio equal to . 22,085 17,712 x 1 Solve for x, rounding to three decimal places. 22,085 17,712 = x 1 1.247 = x Solve for x. Therefore, the ratio of Total Charges for Public Four-Year In-State for 2013-14 to Total Charges for Public Four-Year In-State for 2012-13, with the second quantity scaled to 1, is or to 1. 1.247 1 1.247 (b) Fill in the following ratio table for 2013-14, 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 $15,750 $11,357 $9,204 1 100 Begin with the unknown cells in the third row. A table showing just the second and third rows of the table above, with the unknowns labeled x and y, is shown below. $15,750 $11,357 $9,204 x 1 y Begin by solving for x. Use the ratio table to form a proportion. In setting up a proportion from a ratio table, a value can be compared only to another value in the same row or in the same column. Once that choice is made, the other ratio in the proportion has to be made up in a corresponding fashion. Both and are correct proportions from the ratio table. = x 1 15,750 11,357 = x 15,750 1 11,357 In this case, solve for x because it is easier to simplify, rounding to two decimal places. = x 1 15,750 11,357

1/24/24, 4:07 PM HW 2.1 Ratios and Proportions-Maria Huerta https://tdx.acs.pearsonprd.tech/api/v1/print/highered 2/3 x 1 = 15,750 11,357 x = 1.39 Simplify. The value of x has been added to the table below. Use a similar method to solve for y. $15,750 $11,357 $9,204 1.39 1 y Use the ratio table to form a proportion to solve for y. Both and are correct proportions from the ratio table. = y 1 9,204 11,357 = y 9,204 1 11,357 In this case, solve for y because it is easier to simplify, rounding to two decimal places. = y 1 9,204 11,357 y 1 = 9,204 11,357 y = 0.81 Simplify. Both values have been added to the third row of the table below. Now find the values for the fourth row. Private Room and Board Public Four Year Room and Board In State Public Two Year Room and Board In State $15,750 $11,357 $9,204 1.39 1 0.81 100 To do so, use just the second and fourth rows of the table, shown below. The unknowns have again been labeled with x and y. $15,750 $11,357 $9,204 100 x y Begin by solving for x. Use the ratio table to form a proportion. Both and are correct proportions from the ratio table. = x 100 11,357 15,750 = x 11,357 100 15,750 In this case, solve for x, rounding to two decimal places. = x 100 11,357 15,750 x 100 = 11,357 15,750 x = 11,357 • 100 15,750 Multiply by 100. x = 72.11 Simplify. The value for x has been added to the bottom row of the table below. $15,750 $11,357 $9,204 100 72.11 y Use a similar method to solve for y. Set equal to and solve for y, rounding to two decimal places. y 100 9,204 15,750 y = 58.44 The completed ratio table is shown below.

1/24/24, 4:07 PM HW 2.1 Ratios and Proportions-Maria Huerta https://tdx.acs.pearsonprd.tech/api/v1/print/highered 3/3 1: Table for part (a) 2: Table for part (b) Private Room and Board Public Four Year Room and Board In State Public Two Year Room and Board In State $15,750 $11,357 $9,204 1.39 1 0.81 100 72.11 58.44 Tuition and Fees Room and Board Total Charges Sector 2013 142012 13$ Change% Change 2013 142012 13$ Change% Change 2013 142012 13$ Change% Change Public 2-Year In-State $3,258 $3,162 $96 3.0 $9,204 $7,310 $1894 25.9 $12,462 $10,472 $1,990 19.0 Public 4-Year In-State $10,728 $8,573 $2155 25.1 $11,357 $9,139 $2218 24.3 $22,085 $17,712 $4,373 24.7 Public 4 Year Out of State $26,897 $20,939 $5958 28.5 $11,192 $9,112 $2080 22.8 $38,089 $30,051 $8,038 26.7 Private Nonprofit 4-year $36,999 $28,888 $8111 28.1 $15,750 $10,396 $5354 51.5 $52,749 $39,284 $13,465 34.3 For-Profit $15,104 $15,044 $60 0.4 Private Room and Board Public Four Year Room and Board In State Public Two Year Room and Board In State $15,750 $11,357 $9,204 1 100

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