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The sum of two numbers is 26. the larger of the two numbers is 14 more than three times the smaller number. what are the two numbers?

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2 Answers

x=smaller #
y=larger #
x+y=26
y=3x+14
x+(3x+14)=26
4x+14=26
4x=12
x=3
y=3(3)+14
y=9+14
y=23
answer: 3 and 23
Hi Again Roseland;
Another great question!  I appreciate it!
x=smaller number
y=larger number
 
x+y=26
y=3x+14
 
We need to perform a method called SUBSTITUTION.  I will illustrate.
Let's begin with the first equation, because it is easiest.
Let's isolate for y...
x+y=26
y=26-x
 
Now...
26-x=3x+14
 
Let's combine like terms...
Let's add x to both sides...
x+26-x=3x+14+x
26=4x+14
Let's subtract 14 from both sides...
-14+26=4x+14-14
12=4x
Let's divide both sides by 4...
12/4=(4x)/4
 
x=3
y=26-3=23
 
Let's check our results...
Does y=3x+14
23 ???  3(3)+14
23  ??? 9+14
23=23
Yes!