An online retail store charges a flat shipping fee plus a separate fee per package for bul… — SAT

An online retail store charges a flat shipping fee plus a separate fee per package for bulk deliveries. The total shipping cost, $C$ , in dollars, for an order containing $x$ standard packages and $y$ deluxe packages can be modeled by the equation $C = 15x + 10y + 25$ . If the total shipping cost for a certain order is $195$ dollars and the order contains 8 deluxe packages, how many standard packages are in the order?

6Answer
B
5
C
4
D
8

Answer

The correct answer is 6. Substituting the total cost of

195

for

C

and the 8 deluxe packages for

y

into the equation

C = 15x + 10y + 25

yields

195 = 15x + 10(8) + 25

. Simplifying the equation gives

195 = 15x + 105

. Subtracting 105 from both sides results in

90 = 15x

. Dividing both sides by 15 gives

x = 6

Step-by-Step Solution

Substitute the given values into the linear equation.

Substituting

C = 195

and

y = 8

into the equation

C = 15x + 10y + 25

yields

195 = 15x + 10(8) + 25

This sets up the equation with only one variable,

x

, which we need to solve for.

Simplify the constants on the right side of the equation.

195 = 15x + 80 + 25

, which simplifies to

195 = 15x + 105

Combining like terms simplifies the algebraic expression.

Isolate the variable term

15x

Subtracting 105 from both sides of the equation gives

15x = 195 - 105

, which simplifies to

15x = 90

To solve for

x

, we must isolate the term containing the variable on one side.

Solve for the variable

x

x = \frac{90}{15} = 6

Dividing by the coefficient of

x

isolates the variable completely.

Key Concept

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

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