Question 1203234
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Let x represent the smaller number and y the larger number. 
The sum of the two numbers is 200. If the larger number is 8 less 
than triple the smaller number, what are the two numbers?
The sum of two numbers is 200. But I’m confused as to write if the larger number is 8 less than triple the
X=200-y -> x=200-178.05 smaller #
X=-y+200
Replace y with 178.05
X=-178.05+200
X=21.95
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<pre>
x = smaller unknown number;
y = greater unknown number.


First equation

    x + y = 200   (1)    does not require explanations


Second equation

    y = 3x - 8    (2)    "the larger number is 8 less than triple the smaller number"


To solve, we substitute  y = 3x-8 from equation (2) into equation (1).

In other words, we REPLACE y in equation (1) by this expression  y = 3x-8.  We get then

    x + (3x-8) = 200.


Now we have one equation for one single unknown x.
To solve it, simplify it step by step

    x + 3x - 8 = 200

     4x        = 200+8

     4x        = 208

      x        = 208/4 = 52.


Thus x is just found.  To find y, use equation (2)

    y = 3x-8 = 3*52-8 = 148.


<U>ANSWER</U>.  x= 52,  y= 148,


<U>CHECK</U>.  x + y = 52 + 148 = 200.
</pre>

Solved, checked and explained.


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On the way, you learned how the substitution method works for this problem.