Aboard a research station, Emek and Luna checked the oxygen supply before the next stage of their mission. The station had 5 identical tanks. During earlier experiments, the crew had used 35 liters of oxygen, and the display now showed 290 liters remaining. If x represented the amount originally stored in each tank, Emek wrote the equation 5x - 35 = 290. Luna reversed the operations step by step. She added 35 to both sides to get 5x = 325, then divided both sides by 5 and found x = 65 liters. Before trusting the result, Emek substituted 65 for x: 5(65) - 35 = 290. The check matched the station display exactly. The tanks had originally contained 325 liters altogether, and 290 liters remained. Since the mission plan required at least 280 liters for the next stage, Emek and Luna confirmed that the station had 10 liters more than the required supply and continued their preparations.

Challenges

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Challenge 1 of 5

Challenges

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Challenge 1 of 4
Hint
First represent the original oxygen in all 5 tanks, then account for the 35 liters that were used.
The crew used 35 liters of oxygen and had 290 liters remaining. If x is the original amount in each of the 5 identical tanks, which equation represents this situation?
5x + 35 = 2905x - 35 = 2905(x - 35) = 290x - 35 = 5(290)
Correct. The 5 tanks originally held 5x liters altogether, and 35 liters were then used.
Not quite. Think about how to represent the total amount in 5 identical tanks before subtracting the oxygen that was used.
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Hint
First find how much oxygen remains after the experiment, then isolate 5x.
Suppose the crew completes another experiment using 50 liters from the 290 liters remaining. The next mission stage requires 40 liters to be kept in reserve, and the rest can be divided equally among the 5 tanks for planned tasks. If x is the number of liters available per tank for those tasks, solve 5x + 40 = 290 - 50. What is x?
Correct. There would be 40 liters per tank available for the planned tasks.
Check the amount remaining after 50 liters are used, subtract the 40-liter reserve, and then divide by 5.
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Hint
An equation stays balanced when the same operation is performed on both sides.
Luna solves 5x - 35 = 290 by first adding 35 to both sides. Why is this a valid first step?
Adding 35 changes only the left side, making the equation easier to solve.Adding 35 makes the coefficient of x equal to 1.Adding the same amount to both sides keeps the equation balanced and removes the subtraction of 35.Adding 35 changes 5x into 5(x + 35).
Correct. Adding 35 to both sides preserves equality and leaves 5x by itself on the left.
Not quite. Consider why performing the same operation on both sides preserves the equality.
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Oksijen Tanklarını Dengelemek
TR
ARC_G08_PA_02_STORY_01
Oksijen Tanklarını Dengelemek
Balancing the Oxygen Tanks
EN
ARC_G08_PA_02_STORY_01
Balancing the Oxygen Tanks