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Difficulty: MediumLinear Equations in One Variable

An online store charges a flat shipping fee of 8.508.50 dollars for orders under 100100 dollars. A customer purchases 55 identical shirts and uses a coupon for 12.0012.00 dollars off the total price of the shirts. If the total charge for the order, including shipping, is 86.5086.50 dollars, what is the price, in dollars, of one shirt?

  1. A
    13.2013.20
  2. B
    15.6015.60
  3. 18.0018.00Answer
  4. D
    19.7019.70

Answer

The price of one shirt is 18.0018.00 dollars.
To find the price of one shirt, we set up a linear equation. Let ss represent the price of one shirt. The cost of 55 shirts after applying the 12.0012.00 dollar coupon is 5s−12.005s - 12.00. Since this amount is under 100100 dollars, the flat shipping fee of 8.508.50 dollars is added to the total. This gives the equation 5s−12.00+8.50=86.505s - 12.00 + 8.50 = 86.50. Combining the constants on the left side results in 5s−3.50=86.505s - 3.50 = 86.50. Adding 3.503.50 to both sides yields 5s=90.005s = 90.00. Dividing both sides by 55 gives s=18.00s = 18.00. Thus, the price of one shirt is 18.0018.00 dollars.

Step-by-Step Solution

1
Represent the cost of the shirts using a variable.
Let ss represent the price of one shirt. The cost of 55 shirts with the 12.0012.00 dollar coupon discount is 5s−12.005s - 12.00 dollars.
This establishes the variable for the unknown value we need to find.
2
Set up the full linear equation by including the shipping fee and total charge.
Since 5s−12.005s - 12.00 is under 100100 dollars (which we verify at the end), a flat shipping fee of 8.508.50 dollars applies. The equation is 5s−12.00+8.50=86.505s - 12.00 + 8.50 = 86.50.
This relates all parts of the word problem into a single solvable mathematical statement.
3
Simplify the equation by combining the constant values on the left side.
5s−3.50=86.505s - 3.50 = 86.50
Combining like terms simplifies the algebraic expression.
4
Isolate the variable term by adding 3.503.50 to both sides.
5s=90.005s = 90.00
This moves all constant terms to one side of the equation.
5
Solve for the variable by dividing both sides of the equation by 55.
s=18.00s = 18.00
Dividing by the coefficient of the variable isolates ss to find the final value.

Key Concept

Linear Equations in One Variable
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Topics

Linear Equations in One Variable

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