Math  /  Numbers & Operations

QuestionFormula 10 points Marcelle, your French foreign exchange student, rushes into the kitchen one December morning in a panic. She has heard on the local radio station that the high temperature today will be 420 F . Marcelle is very concerned about this unusually warm temperature during the winter. To calm Marcelle you must "translate' the local temperature into degrees Celsius. What value do you get? Round to two decimal places.
Type your answer...

Studdy Solution

STEP 1

What is this asking? We need to convert 42 degrees Fahrenheit to Celsius. Watch out! Don't mix up the formula!
It's easy to get the addition and subtraction parts wrong.

STEP 2

1. Write down the formula
2. Substitute and solve

STEP 3

The formula to convert Fahrenheit (FF) to Celsius (CC) is: C=59(F32) C = \frac{5}{9} \cdot (F - 32)

STEP 4

This formula reflects the different scales and starting points of Fahrenheit and Celsius.
Celsius sets the freezing point of water at **0** degrees, while Fahrenheit sets it at **32** degrees.
That's why we **subtract 32** from the Fahrenheit temperature first.
The fraction 59\frac{5}{9} accounts for the different scaling between the two systems.
There are **180** degrees between freezing and boiling in Fahrenheit, and **100** degrees between freezing and boiling in Celsius.
The ratio 100180\frac{100}{180} simplifies to 59\frac{5}{9}!

STEP 5

We're given F=42F = 42, so let's plug that into our formula: C=59(4232) C = \frac{5}{9} \cdot (42 - 32)

STEP 6

C=59(10) C = \frac{5}{9} \cdot (10) We **subtract** 3232 from 4242 to get 1010.
This 1010 represents the number of degrees Fahrenheit *above freezing* that we're converting.

STEP 7

C=5910 C = \frac{5}{9} \cdot 10 C=5109 C = \frac{5 \cdot 10}{9} C=509 C = \frac{50}{9} We **multiply** the fraction 59\frac{5}{9} by 1010 to scale the temperature difference to Celsius.

STEP 8

C=5095.56 C = \frac{50}{9} \approx 5.56 We **divide** 5050 by 99 to get our final answer in Celsius.
Rounded to two decimal places, we get **5.56** degrees Celsius.

STEP 9

So, 42 degrees Fahrenheit is equal to approximately **5.56** degrees Celsius.
Tell Marcelle there's no need to panic!
It's a pleasant, cool temperature, perfect for a light jacket, perhaps!

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord