Translate the sentences into math:

x - y = 18 (left side: difference of 2 nums, =: is, 18: 18)

2y + 3x = 74 (twice the smaller: 2y, plus: +, three times the larger: 3x, is: =, 74: 74)

If neither of your math sentences has a variable and nothing else on one side, change it to an equivalent sentence which does (in this case, you probably don't want to do that with the second sentence, because whether you solve for x or y, you will have a fraction to deal with -- sometimes both sentences are like that.

x - y = 18        adding y to both sides will leave x by itself on the left

x = 18 + y So, for this problem x always stands for the same number as 18 added to the number y stands for. In particular it , x, stands for 18 + y in the equation 2y + 3x = 74. so you can SUBSTITUTE one for the other so you get an equation that has y's and numbers, so you can solve for y:

2y + 3(18+y) = 74     multiply out

2y + 54 + 3y = 74   combine like terms on the left, then subtract 54 from both sides

5y = 20     divide both sides by 5

y = 4   if all we wanted was the smaller number, we'd be done. But the question asks what are the numberS? (always go back to the word problem to make sure you have answered the question)

x = 18 + (4) = 22.

So the smaller of the two numbers is 4 and the larger is 22.

Now check IN THE WORD PROBLEM, not in the original math equations. If you translated wrongly, your answers might work just fine, but not work in the word problem.

Is the difference between the two number 18? Yes, 22 - 4 is 18.

Is twice the smaller number plus 3 times the larger, 74? Yes, 2(4) + 3(22) is 8 + 66 = 74.

Now, 1 and 2 should be easier to do.