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Zorluk: OrtaLinear Equations in Two Variables

An online retail store charges a flat shipping fee plus a separate fee per package for bulk deliveries. The total shipping cost, CC, in dollars, for an order containing xx standard packages and yy deluxe packages can be modeled by the equation C=15x+10y+25C = 15x + 10y + 25. If the total shipping cost for a certain order is 195195 dollars and the order contains 8 deluxe packages, how many standard packages are in the order?

  1. 6Cevap
  2. B
    5
  3. C
    4
  4. D
    8

Cevap

6
The correct answer is 6. Substituting the total cost of 195195 for CC and the 8 deluxe packages for yy into the equation C=15x+10y+25C = 15x + 10y + 25 yields 195=15x+10(8)+25195 = 15x + 10(8) + 25. Simplifying the equation gives 195=15x+105195 = 15x + 105. Subtracting 105 from both sides results in 90=15x90 = 15x. Dividing both sides by 15 gives x=6x = 6.

Adım Adım Çözüm

1
Substitute the given values into the linear equation.
Substituting C=195C = 195 and y=8y = 8 into the equation C=15x+10y+25C = 15x + 10y + 25 yields 195=15x+10(8)+25195 = 15x + 10(8) + 25.
This sets up the equation with only one variable, xx, which we need to solve for.
2
Simplify the constants on the right side of the equation.
195=15x+80+25195 = 15x + 80 + 25, which simplifies to 195=15x+105195 = 15x + 105.
Combining like terms simplifies the algebraic expression.
3
Isolate the variable term 15x15x.
Subtracting 105 from both sides of the equation gives 15x=195−10515x = 195 - 105, which simplifies to 15x=9015x = 90.
To solve for xx, we must isolate the term containing the variable on one side.
4
Solve for the variable xx.
x=9015=6x = \frac{90}{15} = 6.
Dividing by the coefficient of xx isolates the variable completely.

Anahtar Kavram

Solving linear equations in two variables by substituting known values and isolating the variable.
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Konular

Linear Equations in Two Variables

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