Ryan S. answered • 02/17/21
University of Houston economics graduate - new to teaching.
Hi Cindy!
Happy to answer and explain this question for you.
The best way to go about this problem is by breaking it down into parts which include the information we know.
Let's start with the first sentence:
The sum of two numbers is 44.
We rewrite this sentence with mathematical language as:
a + b = 44
Where a and b represent the two numbers we don't know. All we know from this first sentence is that adding them together equals 44.
Now for the second sentence:
The smaller number is 12 less than the larger number.
We can also rewrite this sentence using mathematical language as follows:
a - 12 = b
The way we've written it above, a is the larger number and by subtracting 12 from it, the result is b.
What next? Substitution!
We now have two different equations and two variables, which means we have enough information to solve the problem. To do so, we substitute b in the first equation with something that is equivalent to it, a - 12. As shown below:
a + (a - 12) = 44
Now, we need to simplify this equation to give us number a.
a + (a - 12) = 44
Remove the brackets.
a + a - 12 = 44
Add the like terms.
2a - 12 = 44
Add 12 to both sides.
2a = 56
Divide both sides by 2.
a = 28
Now we need to find the number we labeled b. The easiest way to do this is to substitute our result for a into our second equation, which was a - 12 = b.
a - 12 = b
(28) - 12 = b
b = 16
This means our final answer for the two numbers is a = 28 for the larger number and b = 16 for the smaller number.
It's a good idea to double-check our work by substituting our result back into the first equation, too.
a + b = 44
(28) + (16) = 44
44 = 44
And we're all done!
