Find the value of $x$ for which $x$ degrees Fahrenheit is exactly the same as $x$ degrees Celsius (remember the formula for converting Celsius to Fahrenheit is to multiply the Celsius temperature by 9/5 and add 32).

Dabae
Jun 28, 2015

#1**+11 **

F = (9/5)C + 32 (1)

C = (F - 32)(5/9) (2) ....so.....setting (1) = (2), we have

(9/5)C + 32 = (F- 32)(5/9) multiply both sides by (9/5)

(81/25)C + 288/5 = F - 32 add 32 to both sides

(81/25)C + 288/5 + 32 = F

(81/25)C + 448/5 = F (3) and putting (3) into (1), we have

(81/25)C + 448/5 = (9/5)C + 32 simplify

(81/25)C - (9/5)C = 32 - 448/5 ...... (9/5) = (45/25) and 32 = 160/5

(36/25)C = [160 - 448]/5

(36/25)C = [-288/5]

(36/25)C = -1440/25 multiply through by 25

36C = -1440 divide both sides by 36

C = -40 and F = (9/5)(-40) + 32 = -72 + 32 = -40

So....they are equal at -40

CPhill
Jun 28, 2015

#1**+11 **

Best Answer

F = (9/5)C + 32 (1)

C = (F - 32)(5/9) (2) ....so.....setting (1) = (2), we have

(9/5)C + 32 = (F- 32)(5/9) multiply both sides by (9/5)

(81/25)C + 288/5 = F - 32 add 32 to both sides

(81/25)C + 288/5 + 32 = F

(81/25)C + 448/5 = F (3) and putting (3) into (1), we have

(81/25)C + 448/5 = (9/5)C + 32 simplify

(81/25)C - (9/5)C = 32 - 448/5 ...... (9/5) = (45/25) and 32 = 160/5

(36/25)C = [160 - 448]/5

(36/25)C = [-288/5]

(36/25)C = -1440/25 multiply through by 25

36C = -1440 divide both sides by 36

C = -40 and F = (9/5)(-40) + 32 = -72 + 32 = -40

So....they are equal at -40

CPhill
Jun 28, 2015