XMA Equations in F
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ntent/che/onlinerlessonViewer responsive.aspatheader-trues idCourse=149085&idUnit 134147&idLesson-2966319&page 1
LESSON &
Linear Equations in Real-World Scenarios
Linear Equations in Real-World Scenarios Practice Complete this assessment to review what you've learned. It will not count toward your grade.
Two pumps are filling large vats of liquid. One vat is empty, and the pump is filling it at a rate of 6 gallons per minute, other is already filled with 10 gallons, and it is continuing to fill at a rate of 4 gallons per minute. Write an equation to when the two vats will have an equal amount of liquid. Use x as your variable. (1 point)
Let's set up the equation.
The first vat is being filled at a rate of 6 gallons per minute, so the amount of liquid in the first vat can be represented by 6x (since x represents the number of minutes).
The second vat already has 10 gallons and is being filled at a rate of 4 gallons per minute, so the amount of liquid in the second vat can be represented by 10 + 4x.
To find when the two vats will have an equal amount of liquid, we can set up the equation:
6x = 10 + 4x
Simplifying the equation, we get:
2x = 10
Dividing both sides by 2, we get:
x = 5
Therefore, the two vats will have an equal amount of liquid after 5 minutes.
ntent/che/onlinerlessonViewer responsive.aspatheader-trues idCourse=149085&idUnit 134147&idLesson-2966319&page 1
LESSON &
Linear Equations in Real-World Scenarios
Linear Equations in Real-World Scenarios Practice Complete this assessment to review what you've learned. It will not count toward your grade.
Two pumps are filling large vats of liquid. One vat is empty, and the pump is filling it at a rate of 6 gallons per minute, other is already filled with 10 gallons, and it is continuing to fill at a rate of 4 gallons per minute. Write an equation to when the two vats will have an equal amount of liquid. Use x as your variable. (1 point)
To find the time at which the two vats will have an equal amount of liquid, we need to set up an equation based on the given information.
Let's assume the time in minutes is represented by the variable x.
The amount of liquid in the first vat is increasing at a rate of 6 gallons per minute. Therefore, the amount of liquid in the first vat at time x minutes is given by the expression 6x.
The amount of liquid in the second vat is already filled with 10 gallons and is increasing at a rate of 4 gallons per minute. Therefore, the amount of liquid in the second vat at time x minutes is given by the expression 10 + 4x.
To find the time at which the two vats will have an equal amount of liquid, we can set up the equation:
6x = 10 + 4x
Now, let's solve the equation to find the value of x:
6x - 4x = 10
2x = 10
x = 5
Therefore, the two vats will have an equal amount of liquid after 5 minutes.
To solve this problem and write an equation for when the two vats will have an equal amount of liquid, we can first set up equations for each vat based on the given information.
Let x represent the number of minutes it takes for the two vats to have an equal amount of liquid.
For the empty vat being filled at a rate of 6 gallons per minute, we can use the equation:
6x
For the vat already filled with 10 gallons and continuing to fill at a rate of 4 gallons per minute, we can use the equation:
10 + 4x
The equation for when the two vats will have an equal amount of liquid would be:
6x = 10 + 4x
To solve this equation to find the value of x, you can combine like terms and isolate the variable:
6x - 4x = 10
2x = 10
x = 10/2
x = 5
Therefore, the two vats will have an equal amount of liquid after 5 minutes.