Question

(Lesson 11.2) Solve the real-world situation by using the substitution method. (2 points)3. Tank A has 35 gallons of water and is filling up at a rate of 5 gallons per minute. Tank B has 100 gallons ofwater and is draining at a rate of 8 gallons per minute. The system of equations(= 100 – 8xSy = 35 + 5xused to represent this situation. In how many minutes will the tanks contain the same amount of water, andhow much water will that be?can be1

Answer 1

The tanks will have the same amount of water after 5 minutes.

EXPLANATION :

From the problem, we have system of two linear equations :

`\begin{cases}y={35+5x} \\ y={100-8x}\end{cases}`

Where y is the amount of water and x is the time in minutes.

Equate both equations to solve for the time when the tanks contain the same amount of water.

That will be :

`\begin{gathered} 35+5x=100-8x \\ 5x+8x=100-35 \\ 13x=65 \\ x=(65)/(13)=5 \end{gathered}`