DELIVERY TRUCKS

Explanation

To give the right answer we need to analyse the problem

A truck can carry one-ton load (Given)

Now let's sum up all the weights of the materials to be delivered

required delivery = \(\frac12\)-ton sand + \(\frac13\)-ton gravel + \(\frac15\)-ton cement

Now find the LCD of the denominators, which = 2 • 3  • 5 = 30

Multiply the numerators and the denominators as below

$= \frac12 \cdot \frac{15}{15} + \frac13 \cdot \frac{10}{10} + \frac15 \cdot \frac{6}{6}$

Now add the numerators

$\frac{15 + 10 + 6}{30} = \frac{31}{30} = 1\frac{1}{30}$

this is one ton and \(\frac{1}{30}\)-ton, which exceeds the truck capacity.  We cannot deliver all that weight in the truct.