Question

use the following table comparing motor vehicle deaths (mvd) to answer parts (a) through (d) below.

mvd (2021)
mvd per 100,000 people
mvd per 100,000 mv
mvd per 100 million vehicle miles
country a
1,563
3.99
5.7
0.60
country b
2,272
10.16
12.99
1.10

(a) the 1,563 is giving the number of mvd in country a in 2021. solve for the total population of country a in 2021, while the 3.99 is a ratio giving 3.99 mvd : 100,000 people. put this information into a ratio table to find the total population of mvd (2021): 1,563; people: x; mvd per 100,000: 3.99; 100,000
x = 39172932 (round to the nearest integer as needed.)

(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 (2021): 2,272; people: x; mvd per 100,000: 10.16; 100,000
(type integers or decimals.)
solve for x.
x = \boxed{} (round to the nearest integer as needed.)

Explanation:

Part (a)

Step 1: Set up the proportion

We know that the ratio of MVD to population for Country A is \( \frac{3.99}{100000} \) (since 3.99 MVD per 100,000 people) and we have 1563 MVD. Let \( x \) be the population. So we set up the proportion:
\( \frac{3.99}{100000}=\frac{1563}{x} \)

Step 2: Cross - multiply and solve for \( x \)

Cross - multiplying gives us \( 3.99x = 1563\times100000 \)
First, calculate \( 1563\times100000=156300000 \)
Then, solve for \( x \) by dividing both sides by 3.99: \( x=\frac{156300000}{3.99} \)
\( x = 39172932.33\cdots\approx39172932 \) (rounded to the nearest integer)

Part (b)

Step 1: Set up the proportion

The ratio of MVD to population for Country B is \( \frac{10.16}{100000} \) (since 10.16 MVD per 100,000 people) and we have 2272 MVD. Let \( x \) be the population. So we set up the proportion:
\( \frac{10.16}{100000}=\frac{2272}{x} \)

Step 2: Cross - multiply and solve for \( x \)

Cross - multiplying gives us \( 10.16x = 2272\times100000 \)
First, calculate \( 2272\times100000 = 227200000 \)
Then, solve for \( x \) by dividing both sides by 10.16: \( x=\frac{227200000}{10.16} \)
\( x=22362204.72\cdots\approx22362205 \) (rounded to the nearest integer)

Answer:

(a) \( x = 39172932 \)
(b) \( x = 22362205 \)