Given that a+1/(b+(2/c))=17/5, where a is the integer part of the mixed number, and c is the numerator of the fraction part of the mixed number when the mixed number is written in least terms, find the product abc.

Answer 1

a+1/(b+(2/c))=17/5 = 3 + 2/5
So, a natural value to try is a=3
that gives
1/(b+(2/c)) = 2/5
5 = 2(b+2/c)
5c = 2bc+4
c(5-2b) = 4
Now, c can be 4, making b=2
or, c can be -4, making b=3
so, two solutions are (a,b,c) = (3,2,4) or (3,3,-4)
I'm sure there are others.

Answer 2

Evaluate −x+4y when x=−45 and y=13. Write your answer as a fraction or mixed number in simplest form.

Answer 3

17/5 = 3 2/5

a+1/(b+(2/c)) = 3 2/5, which means:
a = 3

Now we have:
1/(b+(2/c)) = 2/5 (multiply everything by c)
c/(bc+2) = 2/5 (the two c’s in 2c/5c cancel out), which means:
c = 2

Now we’re left with:
bc+2 = 5
bc = 3 (substitute the value we got for c)
b(2) = 3
b = 1.5

Finally, abc = 3(2)(1.5) = 9