The length L, in centimeters, of a copper rod at a temperature of T degrees Celsius can be… — ACT

The length $L$ , in centimeters, of a copper rod at a temperature of $T$ degrees Celsius can be modeled by the linear equation $L = 150.04 + 0.012T$ . If the length of the rod is measured to be $150.40$ centimeters, what is its temperature in degrees Celsius?

Answer: 30 degrees Celsius

Answer

The temperature of the rod is 30 degrees Celsius.

The correct answer is 30. By substituting the given length of

150.40

centimeters into the equation for

L

, we get

150.40 = 150.04 + 0.012T

. Subtracting

150.04

from both sides gives

0.36 = 0.012T

. Finally, dividing both sides by

0.012

yields the temperature

T = 30

degrees Celsius.

Step-by-Step Solution

Substitute the measured length

L = 150.40

into the equation.

150.40 = 150.04 + 0.012T

To set up the equation with the given value for length.

Subtract 150.04 from both sides of the equation.

0.36 = 0.012T

To isolate the variable term containing

T

Divide both sides of the equation by 0.012.

T = 30

To find the temperature

T

Key Concept

Solving a multi-step linear equation involving decimals

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