Questions: The total cost of a pair of shoes and a tie was 59.91. If the price of the pair of shoes was 1.11 less than the tie, what was the price of the pair of shoes? Express your answer as a simplified fraction or a decimal rounded to two places.

$The total cost of a pair of shoes and a tie was 59.91. If the price of the pair of shoes was 1.11 less than the tie, what was the price of the pair of shoes? Express your answer as a simplified fraction or a decimal rounded to two places.$

Transcript text: The total cost of a pair of shoes and a tie was $\$ 59.91$. If the price of the pair of shoes was $\$ 1.11$ less than the tie, what was the price of the pair of shoes? Express your answer as a simplified fraction or a decimal rounded to two places.

Solution

Solution Steps

To find the price of the pair of shoes, we can set up a system of equations. Let $ x $ be the price of the tie. Then, the price of the shoes is $ x - 1.11 $. The total cost is given as $59.91. We can solve the equation $ x + (x - 1.11) = 59.91 $ to find $ x $, and then calculate the price of the shoes.

Step 1: Set Up the Equations

Let $ x $ be the price of the tie. The price of the shoes can be expressed as $ x - 1.11 $. The total cost of the shoes and the tie is given by the equation: \[ x + (x - 1.11) = 59.91 \]

Step 2: Simplify the Equation

Combining the terms in the equation, we have: \[ 2x - 1.11 = 59.91 \]

Step 3: Solve for $ x $

Adding $ 1.11 $ to both sides gives: \[ 2x = 59.91 + 1.11 = 61.02 \] Dividing both sides by $ 2 $ results in: \[ x = \frac{61.02}{2} = 30.51 \]

Step 4: Calculate the Price of the Shoes

Now, substituting $ x $ back to find the price of the shoes: \[ \text{Price of shoes} = x - 1.11 = 30.51 - 1.11 = 29.40 \]