Answer:
Large number: 20
Small number: 12
Step-by-step explanation:
Hello!
This problem is a word problem, and if we assign variables to find each of the numbers, it could help.
A variable is usually an unknown number that stands for that unknown.
Since in this problem we know there is a small and large number, let's assign the large number as the variable x and small number as variable y.
For the first part, it says two numbers whose difference is 8, which means the large number minus the smaller number equals 8.
x-y=8
For the second part is tricky. It's saying that the small number times three is 16 more than the large number itself. When constructing a equation, this is what we get:
x+16=3y x plus 16 equals 3 times y
To solve this equation together so we can make it super easy, let's do the method of substitution, which is where we make an equation equal to a variable and input that equation into the second equation.
We can use x-y=8 to input, we can rearrange y and plug it to the right side to get x=8+y
Since x equals 8+y, let's input this into the second equation.
(8+y)+16=3y input the rearranged equation into the second
24+y=3y combine like terms
-y -y
24=2y divide by two to get y by itself
12=y
We aren't done yet! We have to find x still; let's use the previous first equation to find x. We know y=12, so let's plug it in.
x-y=8 original formula
x-12=8 plug it in
+12 +12
x=20
Therefore, the large number is 20, and smaller number is 12.
