[math](\text{-}8.7)(1.4)=a[/math]
[math]\text{-}8.7b=1.4[/math]
[math]\text{-}8.7+c=\text{-}1.4[/math]
[math]\text{-}8.7-d=\text{-}1.4[/math]
[list][*]Explain what the variable represents in the situation.[br][/*][*]Determine the value of the variable that makes the equation true, and explain your reasoning.[/*][/list][br]Situation 1
A penguin is standing 3 feet above sea level and then dives down 10 feet. [br]What is its depth?
A dolphin is swimming 3 feet below sea level and then jumps up 10 feet. [br]What is its height at the top of the jump?
A sea turtle is swimming 3 feet below sea level and then dives down 10 feet. [br]What is its depth?
An eagle is flying 10 feet above sea level and then dives down to 3 feet above sea level. [br]What was its change in altitude?
A pelican is flying 10 feet above sea level and then dives down reaching 3 feet below sea level.[br]What was its change in altitude?
A shark is swimming 10 feet below sea level and then swims up reaching 3 feet below sea level. [br]What was its change in depth?
[list][*]An equation that represents your situation[br][/*][*]What your variable and each term in the equation represent[br][/*][*]How the operations in the equation represent the relationships in the story[br][/*][*]How you use inverses to solve for the unknown quantity[br][/*][*]The solution to your equation[br][/*][/list][br][size=150]Situations:[/size][br][list=1][*]As a [math]7\frac{1}{4}[/math] inch candle burns down, its height decreases [math]\frac{3}{4}[/math] inch each hour. How many hours does it take for the candle to burn completely?[/*][*]On Monday [math]\frac{1}{9}[/math] of the enrolled students in a school were absent. There were 4,512 students present. How many students are enrolled at the school?[/*][*]A hiker begins at sea level and descents 25 feet every minute. How long will it take to get to an elevation of -750 feet?[/*][*]Jada practices the violin for the same amount of time every day. On Tuesday she practices for 35 minutes. How much does Jada practice in a week?[/*][*]The temperature has been dropping [math]2\frac{1}{2}[/math] degrees every hour and the current temperature is [math]-15^{^\circ}F[/math]. How many hours ago was the temperature [math]0^{^\circ}F[/math]?[/*][*]The population of a school increased by 12%, and now the population is 476. What was the population before the increase?[br][/*][*]During a 5% off sale, Diego pays $74.10 for a new hockey stick. What was the original price?[br][/*][*]A store buys sweaters for $8 and sells them for $26. How many sweaters does the store need to sell to make a profit of $990?[/*][/list]
[size=150][size=100]Diego and Elena are 2 miles apart and begin walking towards each other. Diego walks at a rate of 3.7 miles per hour and Elena walks 4.3 miles per hour. While they are walking, Elena's dog runs back and forth between the two of them, at a rate of 6 miles per hour. [/size][/size]Assuming the dog does not lose any time in turning around, how far has the dog run by the time Diego and Elena reach each other?