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# Find the value of \$x\$ for which \$x\$ degrees Fahrenheit is exactly the same as \$x\$ degrees Celsius (remember the formula for converting Celsi

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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
+80931
+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
Sort:

#1
+80931
+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

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