Unit 5, Lesson 16
Representing Contexts with Equations
Grade 7
Practice
Problem 1
Match each situation to one of the equations.
A whale was diving at a rate of 2 meters per second. How long will it take for the whale to get from the surface of the ocean to an elevation of -12 meters at that rate?
A swimmer dove below the surface of the ocean. After 2 minutes, she was 12 meters below the surface. At what rate was she diving?
The temperature was -12 degrees Celsius and rose to 2 degrees Celsius. What was the change in temperature?
The temperature was 2 degrees Celsius and fell to -12 degrees Celsius. What was the change in temperature?
\(\text-12 + x = 2\)
\(2 + x = \text-12\)
\(\text-2x = \text-12\)
Problem 2
Starting at noon, the temperature dropped steadily at a rate of 0.8 degrees Celsius every hour.
For each of these situations, write and solve an equation, and describe what the variable represents.
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How many hours did it take for the temperature to decrease by 4.4 degrees Celsius?
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If the temperature after the 4.4-degree drop was -2.5 degrees Celsius, what was the temperature at noon?
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Problem 3
The markings on the number line are evenly spaced. Label the other markings on the number line.
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Problem 4
Find the value of each expression.
- \(12 + \text-10\)
- \(\text-5 - 6\)
- \(\text-42 + 17\)
- \(35 - \text-8\)
- \(\text-4\frac12 + 3\)
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Problem 5
Kiran mixes \(\frac34\) cup of raisins, 1 cup peanuts, and \(\frac12\) cup of chocolate chips to make trail mix. How much of each ingredient would he need to make 10 cups of trail mix? Explain your reasoning.
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