SOLUTION: if tom, james, and tony buy an 18in. sandwich. tom gives james one half of what tom gets and tony gets three fourths of what tom gets. what is the length of each persons sandwich.

Algebra ->  Human-and-algebraic-language -> SOLUTION: if tom, james, and tony buy an 18in. sandwich. tom gives james one half of what tom gets and tony gets three fourths of what tom gets. what is the length of each persons sandwich.       Log On


   

Question 241393: if tom, james, and tony buy an 18in. sandwich. tom gives james one half of what tom gets and tony gets three fourths of what tom gets. what is the length of each persons sandwich.
Answer by College Student(505) About Me  (Show Source):
You can put this solution on YOUR website!
Let Tom = x
James = 1/2 x
Tony = 3/4 x
Total lenght of sandwich = 18 inches
.
Our equation now becomes: x%2B%28%281%2F2%29x%29%2B%28%283%2F4%29x%29=18
Since your denominators are 1, 2, and 4... the LCD is 4.
The new equation with common denominators becomes:
%28%284%2F4%29x%29%2B%28%282%2F2%29%281%2F2%29x%29%2B%28%283%2F4%29x%29=18
%284%2F4%29x%2B%282%2F4%29x%2B%283%2F4%29x=18
%28%284%2F4%29%2B%282%2F4%29%2B%283%2F4%29%29x=18
Then add numerators:
%289%2F4%29x=18
Now multiply by the fraction's reciprocal on both sides to determine the value of x.
x=18%284%2F9%29
x=72%2F9
x=8
.
Tom's sandwich is 8 inches long.
James's sandwich is (1/2)*8=4 inches long.
Tony's sandwich is (3/4)*8=6 inches long.
.
If we add all pieces, we get:
8%2B4%2B6=18