The sum of two numbers is 54. The smaller number is 18 less than the larger number. What are the numbers?

The larger number is 37.  This makes the smaller number 56 - 37, which is 19.

Step-by-step explanation:

The first step is to pick variables for the two numbers.  Lets call the smaller number x and the larger number y.

Since the sum of the two numbers is 56, this means that x + y = 56.  Let's call this equation 1 and save it for later.

The next sentence says:

The smaller number is 18 less than the larger number.  So, 18 less than the larger number would be y - 18.  So, the smaller number must be equal to this, so

x = y - 18

Replace the x in equation 1 with y - 18

x + y = 56

(y-18) + y = 56   (replace x with y-18)

2y - 18 = 56        (add the y's)

2y = 74               (add 18 to both sides)

y = 37                 (divide both sides by 2)

So, the larger number is 37.  This makes the smaller number 56 - 37, which is 19.

Hope this helps!!  :)

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step-by-step explanation:

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