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Zorluk: OrtaInterpreting Linear Relationships in Context

An agricultural irrigation system draws water from a storage tank at a constant rate. The volume of water, VV, in gallons, remaining in the tank mm minutes after the irrigation begins is given by the equation V=12,000−45mV = 12,000 - 45m. According to the model, after how many minutes of irrigation will there be exactly 8,4008,400 gallons of water remaining in the tank?

Cevap: 80 minutes

Cevap

The irrigation system will have exactly 8,4008,400 gallons of water remaining after 8080 minutes.
To find the number of minutes, mm, when the volume of water remaining is exactly 8,4008,400 gallons, substitute 8,4008,400 for VV in the given linear model: 8,400=12,000−45m8,400 = 12,000 - 45m. Subtracting 12,00012,000 from both sides of the equation yields −3,600=−45m-3,600 = -45m. Dividing both sides of the equation by −45-45 yields m=80m = 80. Therefore, after 8080 minutes, there will be exactly 8,4008,400 gallons of water remaining in the tank.

Adım Adım Çözüm

1
Substitute the target volume of 8,4008,400 gallons for VV in the linear model equation.
8,400=12,000−45m8,400 = 12,000 - 45m
We want to find the number of minutes, mm, when the remaining volume, VV, is exactly 8,4008,400 gallons.
2
Subtract 12,00012,000 from both sides of the equation.
−3,600=−45m-3,600 = -45m
This isolates the variable term −45m-45m on one side of the equation.
3
Divide both sides by −45-45 to solve for mm.
m=80m = 80
This isolates mm to find the number of minutes elapsed.

Anahtar Kavram

Solving linear equations in context
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Konular

Interpreting Linear Relationships in Context

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