The larger of two positive integers is three more than the smaller. If twice the square of the smaller integer is
increased by three times the larger integer, the result is 74.
Find the integers. [Only an algebraic solution will be
accepted.]

y=x+4

Step-by-step explanation:

So, let's start with the fact that we have two numbers. Let's call one of them "x" and the other one "y." Let's also assume that "y" is the larger number and "x" is the smaller number.

We know that both of them added together (the sum) gives us 74. Mathematically, that means:

x+y=74.

We also know that the larger number ("y") is 4 more than the smaller number ("x"). Another way to say this is, if you have the smaller number and add 4 more to it, you'll end up with the larger number. Mathematically, this means:

y=x+4

Since we know that y=x+4, we can put "x+4" into the first equation for "y", giving us:

x+(x+4)=74

Simplifying gives us:

2x+4=74

   -4   -4

2x=70

---  ---

2    2

x=35

Since we now know that x=35, and we know that y=x+4, we now know that:

y=(35)+4

y=39

Now that we have both of the numbers, we should check our work to ensure it's correct:

Does 39+35=74?      Yes it does.

Is 39 (the larger of the two numbers) four more than the smallest number (35)?    Yes it is.