Math Problem Statement

Use the following table comparing motor vehicle deaths​ (MVD) to answer parts​ (a) through​ (d) below. MVD left parenthesis 2021 right parenthesis Start 2 By 1 Matrix 1st Row 1st Column MVD per 2nd Row 1st Column 100 comma 000 people EndMatrix

Start 2 By 1 Matrix 1st Row 1st Column MVD per 2nd Row 1st Column 100 comma 000 MV EndMatrix

Start 3 By 1 Matrix 1st Row 1st Column MVD per 2nd Row 1st Column 100 million 3rd Row 1st Column vehicle miles EndMatrix

Country A 1 comma 698 3.13 5.8 0.50 Country B 2 comma 110 9.79 13.33 1.50 Question content area bottom Part 1 ​(a) The 1 comma 698 is giving the number of MVD in Country A for their entire​ population, while the 3.13 is a ratio giving 3.13 MVD​ : 100,000 people. Put this information into a ratio table to find the total population of Country A in 2021. Solve for the total population. MVD left parenthesis 2021 right parenthesis People 1 comma 698 x 3.13 ​100,000 xequals    54,249,201 ​(Round to the nearest integer as​ needed.) Part 2 ​(b) Use the same technique to find the population of Country B in​ 2021, by first filling in the bottom row of the table and then solving for x. MVD left parenthesis 2021 right parenthesis People 2 comma 110 x    9.79    100,000 ​(Type integers or​ decimals.) Part 3 Solve for x. xequals select: 21,552,605 21,552,605 ​(Round to the nearest integer as​ needed.) Part 4 ​(c) How many motor vehicles​ (MV) were there in Country B in​ 2021? select: 15,828,957 15,828,957 ​(Round to the nearest integer as​ needed.) Part 5 ​(d) Compute the ratio of the number of motor vehicles in Country A in 2021 to the number of motor vehicles in the Country B in 2021 and scale the second quantity to 1. The ratio is    enter your response here to 1. ​(Type an integer or decimal rounded to one decimal place as​ needed.)

Solution

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Math Problem Analysis

Mathematical Concepts

Ratios
Proportions
Cross-multiplication
Population Estimation

Formulas

Ratio equation: MVD/Population = Death Rate/100,000 people
Cross-multiplication: MVD × 100,000 = Death Rate × Population
Vehicle estimation: MVD/Number of Vehicles = Death Rate per 100,000 vehicles

Theorems

Proportional Reasoning
Cross-multiplication

Suitable Grade Level

Grades 10-12