Substitution Worksheet With Answer Key - Waynesville R-Vi School District Page 20

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Since x
6-2 Substitution
equal to the demand for nurses was during 1996.
The table shows the approximate number of tourists in two areas of the world during a
recent year and the average rates of change in tourism.
a. Define the variables, and write an equation for each region s tourism rate.
b. If the trends continue, in how many years would you expect the number of tourists in the regions to be equal?
a. Let x = number of years, and y = number of tourists in millions. So, the South America and Caribbean tourism rate
is y = 0.8x + 40.3 and the Middle East is y = 1.8x + 17.0.
b. y = 0.8x + 40.3
y = 1.8x + 17.0
Substitute 0.8x + 40.3 for y in the second equation.
So, in 23.3 years, or about 23 years 4 months, the number of tourists in South America and the Caribbean will be
equal to the number of tourists in the Middle East.
The table shows the winning times for the Triathlon World Championship.
a. The times are in hours, minutes, and seconds. Rewrite the times rounded to the nearest minute.
b. Let the year 2000 be 0. Assume that the rate of change remains the same for years after 2000. Write an equation
to represent each of the men s and women s winning times y in any year x.
c. If the trend continues, when would you expect the men s and women s winning times to be the same? Explain
your reasoning.
) min or about 111 min.
a.
1:44:51 represents 1 hr 44 min 51 sec = (60 + 44 +
Page 20
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1:54:43 represents 1 hr 54 min 43 sec = (60 + 54 +
) min or about 115 min.
1:59:14 represents 1 hr 59 min 14 sec = (60 + 59 +
) min or about 119 min.

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