Question 241393
Let Tom = x
James = 1/2 x
Tony = 3/4 x
Total lenght of sandwich = 18 inches
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Our equation now becomes: {{{x+((1/2)x)+((3/4)x)=18}}}
Since your denominators are 1, 2, and 4... the LCD is 4.
The new equation with common denominators becomes:
{{{((4/4)x)+((2/2)(1/2)x)+((3/4)x)=18}}}
{{{(4/4)x+(2/4)x+(3/4)x=18}}}
{{{((4/4)+(2/4)+(3/4))x=18}}}
Then add numerators:
{{{(9/4)x=18}}}
Now multiply by the fraction's reciprocal on both sides to determine the value of x.
{{{x=18(4/9)}}}
{{{x=72/9}}}
{{{x=8}}}
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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.
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If we add all pieces, we get:
{{{8+4+6=18}}}