Question

noahs oven thermometer gives a reading that is 2% greater than the actual temperature.
a. if the actual temperature is 325° f, what will the thermometer reading be?

b. if the thermometer reading is 76° f, what is the actual temperature? round to the nearest tenth of degrees fahrenheit.

Explanation:

Part a

Step1: Understand the percentage increase

The thermometer reading is 2% greater than the actual temperature. So we need to find 2% of 325 and add it to 325. First, calculate 2% of 325. 2% can be written as 0.02 in decimal. So 2% of 325 is $0.02\times325$.

Step2: Calculate the increase and total reading

$0.02\times325 = 6.5$. Then the thermometer reading is the actual temperature plus the increase, so $325 + 6.5 = 331.5$.

Part b

Step1: Set up the equation for actual temperature

Let the actual temperature be $x$. The thermometer reading is 2% greater than $x$, so the thermometer reading is $x + 0.02x = 1.02x$. We know the thermometer reading is 76, so we have the equation $1.02x = 76$.

Step2: Solve for x

To find $x$, we divide both sides of the equation by 1.02. So $x=\frac{76}{1.02}\approx74.5$ (rounded to the nearest tenth).

Answer:

a. $\boldsymbol{331.5}$
b. $\boldsymbol{74.5}$