Eliminate a variable

[Tinopo]

Hi, I have this: h=2C-34 where h is an amount of icecream being sold and C is temperature centigrade.
I also have this: 5/9F-32 where centigrade is converted to Fahrenheit.
So i can substitude the second formula in the first one: h=2(5/9F-32)-34
I get that, but the answer is: h= 10/9F + 14/9
Please anyone explain me how the 14/9 came about?
Thank you.

 

[lev888]

Hi, I have this: h=2C-34 where h is an amount of icecream being sold and C is temperature centigrade.
I also have this: 5/9F-32 where centigrade is converted to Fahrenheit.
So i can substitude the second formula in the first one: h=2(5/9F-32)-34
I get that, but the answer is: h= 10/9F + 14/9
Please anyone explain me how the 14/9 came about?
Thank you.

I don't see where it comes from.

 

[Tinopo]

Thanks for answering. I dont see it either. It's very frustatrating. I'll skip the question.

 

[JeffM]

I know exactly how the 14/9 came about: there is confusion somewhere about signs. In addition, you did not tell us what you got, which may have had a separate error because you seem to have been using the wrong conversion formula.

[MATH]h = 2c + 34 \text { and } c = 5(f - 32)/9 \implies \\ h =2\{5(f - 32)/9\} + 34 = \dfrac{10f - 320}{9} + 34 =\\ \dfrac{10f - 320}{9} + \dfrac{306}{9} = \dfrac{10f}{9} - \dfrac{14}{9}.[/MATH]First, I'd check that the problem and answer key have the signs indicated in my working. If not, there is a typo in your book.

Second, I'd recognize that your conversion formula is wrong. It is c = 5 * (f - 32)/9, not c = 5/9f - 32. [.......................edited]

 

[Cubist]

Second, I'd recognize that your conversion formula is wrong. It is c = 5 * (f - 32)/9, not c = 5/9f - 32. [.......................edited]

A slight omission from the above, c = 5(f - 32)/9. [.......................fixed]

I guess that the conversion should have been written 5/9(F-32) rather than the 5/9F-32 quoted by @Tinopo

 

[Tinopo]

I know exactly how the 14/9 came about: there is confusion somewhere about signs. In addition, you did not tell us what you got, which may have had a separate error because you seem to have been using the wrong conversion formula.

[MATH]h = 2c + 34 \text { and } c = 5(f - 32)/9 \implies \\ h =2\{5(f - 32)/9\} + 34 = \dfrac{10f - 320}{9} + 34 =\\ \dfrac{10f - 320}{9} + \dfrac{306}{9} = \dfrac{10f}{9} - \dfrac{14}{9}.[/MATH]First, I'd check that the problem and answer key have the signs indicated in my working. If not, there is a typo in your book.

Second, I'd recognize that your conversion formula is wrong. It is c = 5 * (f - 32)/9, not c = 5/9f - 32. [.......................edited]

Thank you!!