Question

Cal installs new tires and gets paid \(\$ 1.17\) per tire or gets paid \(\$ 10.50\) per hour for 8 hours, whichever is greater. How much more does he make on a day when he installs 85 tires than he would make if he received just his hourly wage? A. \(\$ 9.36\) B. \(\$ 10.50\) C. \(\$ 12.43\) D. \(\$ 15.45\)

Short answer

\(\$15.45\)

Step-by-step solution

Calculate daily earnings from installing tires

For each tire, Cal earns \(\$ 1.17\). If he installs 85 tires in a day, the total earnings from the tires can be calculated as: \(85 \times \$ 1.17 = \$ 99.45\).

Calculate daily earnings from hourly wage

Cal's hourly wage is \(\$ 10.50\) and he works for 8 hours. The total earnings from working hours can be calculated as: \(8 \times \$ 10.50 = \$ 84\).

Compare both earnings

Now, compare the earnings from installing tires and hourly wage. From tires, he earns \(\( 99.45 \) and from the hourly wage, he earns \(\) 84 \). Clearly, \(\( 99.45 \) is greater than \(\) 84 \).

Calculate the difference

To find out how much more Cal makes from installing tires than from his hourly wage, subtract his hourly earnings from his tire earnings: \(\$ 99.45 - \$ 84 = \$ 15.45\).

Key concepts

Earnings Calculation

Calculating earnings is essential to understanding the overall income based on various payment methods. In this problem, Cal can either get paid per tire he installs or receive a fixed hourly wage for his work.

When calculating earnings per tire, multiply the number of tires installed by the payment per tire. Mathematically, this can be expressed as \( \text{Total earnings from tires} = \text{number of tires} \times \text{payment per tire} \).

For hourly wages, you need to take the number of hours worked and multiply it by the hourly wage rate. The formula is \( \text{Total earnings from hourly wage} = \text{hours worked} \times \text{hourly wage} \).

In Cal's case, he earns \(1.17 per tire, and if he installs 85 tires in a day, his total earnings would be \( 85 \times 1.17 = 99.45 \).

Calculating his hourly wage, if he works 8 hours a day and earns \)10.50 per hour, his total daily income from hourly wage would be \( 8 \times 10.50 = 84 \).

Comparison of Earnings

In any scenario involving multiple payment options, it's vital to compare the potential outcomes to determine the best choice. Here, Cal can either get paid based on the number of tires he installs or by his hourly wage.

Use the previously calculated earnings to compare the two methods. From tire installation, Cal earns \(99.45, and from hourly wage, he earns \)84 a day.

Clearly, \(99.45 is greater than \)84. Therefore, installing tires provides Cal with a higher income for that day.

By comparing the amounts, Cal can determine the most profitable option. This process of comparing earnings helps in making informed financial decisions.

Multiplication and Subtraction

For solving the problem, we use basic arithmetic operations like multiplication and subtraction.

Multiplication helps in calculating the total earnings from individual units, such as tires or time worked.

For tires, the multiplication was \( 85 \times 1.17 = 99.45 \). For hourly wages, it was \( 8 \times 10.50 = 84 \).

Subtraction is useful to find the difference between two values. We used it to determine how much more Cal earns from installing tires compared to his hourly wage.

The calculation was \( 99.45 - 84 = 15.45 \). Thus, Cal makes $15.45 more by installing tires than by his hourly wage.

Understanding these basic operations within the context of earnings calculation helps in solving similar problems effectively and efficiently.