Reuben rented a truck for one day. There was a base fee of $20.95, and there was an additional charge of 98 cents for each mile
1 answer:
The number of miles did Reuben drive the truck, with the base fee of $20.95, and an additional charge of 98 cents for each mile driven is 287 miles.
<h3 /><h3>What is the equation of variable?</h3>The variable is the unknown part of the equation. Variable changes withe change in the quantities for any situation.
Properties of a equation-
- Equations are the expressions which consist of the variables, coefficients of variables and constants.
- The equations are used to represent the general problem in the mathematical way to solve them.
- The equation is used to show the relationship between the variables of the equation and the quantities in a situation.
Reuben rented a truck for one day. There was a base fee of $20.95, and there was an additional charge of 98 cents for each mile driven.
Reuben had to pay $302.21 when he returned the truck. Suppose the Reuben drive the truck for x miles. Thus,
Solve the equation to find the number of miles he drives,
Thus, the number of miles did Reuben drive the truck, with the base fee of $20.95, and an additional charge of 98 cents for each mile driven is 287 miles.
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Answer:
Ok, we have a system of equations:
6*x + 3*y = 6*x*y
2*x + 4*y = 5*x*y
First, we want to isolate one of the variables,
As we have almost the same expression (x*y) in the right side of both equations, we can see the quotient between the two equations:
(6*x + 3*y)/(2*x + 4*y) = 6/5
now we isolate one off the variables:
6*x + 3*y = (6/5)*(2*x + 4*y) = (12/5)*x + (24/5)*y
x*(6 - 12/5) = y*(24/5 - 3)
x = y*(24/5 - 3)/(6 - 12/5) = 0.5*y
Now we can replace it in the first equation:
6*x + 3*y = 6*x*y
6*(0.5*y) + 3*y = 6*(0.5*y)*y
3*y + 3*y = 3*y^2
3*y^2 - 6*y = 0
Now we can find the solutions of that quadratic equation as:
So we have two solutions
y = 0
y = 2.
Suppose that we select the solution y = 0
Then, using one of the equations we can find the value of x:
2*x + 4*0 = 5*x*0
2*x = 0
x = 0
(0, 0) is a solution
if we select the other solution, y = 2.
2*x + 4*2 = 5*x*2
2*x + 8 = 10*x
8 = (10 - 2)*x = 8x
x = 1.
(1, 2) is other solution