First, it would be wise to choose two variables to help us differentiate between the two numbers. I will choose "a" for the first number and "b" for the second.
Next, we would take each sentence to write an equation.
"The sum of two numbers is 108." The word sum implies that we would add the two numbers, and the result of adding would be 108. Therefore, a + b = 108.
"One number is eight times the other number." Because this word problem does not specify if a or b is bigger, we can use either to form a relationship. Eight times implies that we would multiply one of the numbers by 8, and the result would be the other number. Therefore, 8a = b.
Since we now have two equations that relate both of our variables, or numbers, we can use the rules of substitution to find our solutions. The second equation tells us that 8a = b, so I can use the 8a to replace b in the first equation, giving us a + 8a = 108.
We would then use the rules for solving equations with one variable to solve.
a + 8a = 108
Combine like terms: a + 8a = 9a
9a = 108
Isolate the variable by dividing both sides by 9: (9a / 9) = (108 / 9)
This gives us an a value of 12.
To find b, we could use either equation and substitute our newly-found a-value in. We established in the second equation that our other number, b, would equal eight times the a. So, b = 8 * 12, which would be 96.
The numbers would be 12 and 96. I hope this helps!
Krystal S.
09/17/20
Alex C.
Thank you legit soooo much :)09/17/20