Solving Word Problems With Equations

Quote:

Originally Posted by larry21

Determine the following numbers.

Two consecutive integers with half of the small equal to 4 more than one third of the larger.

My work:

Let the value of 1st integer be x(1/2)
Let the value of 2nd integer be x+1(1/3)+4

x(1/2) = x+1(1/3)+4

...Am I right so far? If so, I have no idea how to solve this?

Help appreciated. Word problems are very hard for me. Thank you.

Well we have two consecutive integers, which means that the larger number is equal to the smaller number plus one. If we let the smaller number equal $x$ , we can write

$\frac{x}{2}=\frac{x+1}{3}+4$

which might be the same as what you wrote, except that you should have written parentheses around (x+1).

This is not a very complicated problem; multiply through by 6 (which is the least common multiple of 2 and 3) to get

$3x = 2(x+1)+24$

Does it look more solvable now?