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Monica’s school band held a car wash to raise money for a trip to a parade in New York City. After washing 125 cars, they made $775 from a combination of $5.00 quick washes and $8.00 premium washes. This system of equations models the situation. x + y =125 5x + 8y = 775 Solve the system to answer the questions. How many premium car washes were ordered? premium car washes How many quick car washes were ordered? quick car washes

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The two equations are:

[tex]x+y=125[/tex]  and

[tex]5x+8y=775[/tex]

Where, x is the number of quick car washes and y is the number of premium car washes.

Multiplying the first equation by -5 we have:

[tex](-5)*[x+y=125]\\=-5x-5y=-625[/tex]

Now adding this to the second equation and then solving for y, we have:

[tex]3y=150\\y=\frac{150}{3}\\y=50[/tex]

Now, taking y = 50 and putting it in any one of the original equations (let's put in the first one) will give us x.

[tex]x+y=125\\x+50=125\\x=125-50\\x=75[/tex]

Hence, there was 50 premium car washes and 75 quick car washes.


ANSWER:

"How many premium car washes were ordered?" 50

"How many quick car washes were ordered?" 75

You can use the given equations to find the value of unknown variables x and y which represents the number of quick washes and premium washes.

  • Number of premium car washes ordered = y = 50
  • Number of quick car washes ordered = x = 75

How to find the solution to the given system of equation?

For that , we will try solving it first using the method of substitution in which we express one variable in other variable's form and then you can substitute this value in other equation to get linear equation in one variable.

If there comes a = a situation for any a, then there are infinite solutions.

If there comes wrong equality, say for example, 3=2, then there are no solutions, else there is one unique solution to the given system of equations.

Using the above method to solve the obtained system of equations

The system of equation we have is

[tex]x + y = 125\\5x + 8y = 775[/tex]

where,

x = number of quick car washes

y = number of premium car washes

Using the method of substitution:

Finding x in terms of y from first equation:

[tex]x + y = 125\\x = 125 - y[/tex]

Substituting this value of x in the second equation, we get

[tex]5x + 8y = 775\\5(125 - y) + 8y = 775\\625 + 3y = 775\\3y = 775 - 625\\\\y = \dfrac{150}{3} = 50[/tex]

Substituting this value in the first expression found for x, we get

[tex]x = 125 - y\\x = 125 - 50 = 75[/tex]

Thus, we have:

  • Number of premium car washes ordered = y = 50
  • Number of quick car washes ordered = x = 75

Learn more here about system of linear equations here:

https://brainly.com/question/13722693

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