Mark B. answered • 11/19/17
Tutor
New to Wyzant
PhD Candidate in Psychology: Experienced Math, Statistics, Tutor
Hello Mo,
Okay, let's solve this and see if we can get you along here.
Allow the two numbers in your problem to be represented as follows:
x = one number
y = another number
Now we need to write the equation premised on the information we have but we have an intermediate step to take here, don't we?
We are told the two numbers have a sum of 41, correct?
Okay, let's solve this and see if we can get you along here.
Allow the two numbers in your problem to be represented as follows:
x = one number
y = another number
Now we need to write the equation premised on the information we have but we have an intermediate step to take here, don't we?
We are told the two numbers have a sum of 41, correct?
Therefore:
x + y = 41 All we have done here is expressed what the problem is telling us, right?
The other condition, that the difference between the two is 7, needs to be met too.
Therefore:
x - y = 7
So, the two equations are:
x + y = 41
x - y = 7
Now add the two equations.
x + y = 41
x - y = 7
_________
2x = 48
x = 48/2 correct OR
x = 24
Please note: I am adding the two equations because I can ELIMINATE the y variable by doing so. We will not always be this fortunate with some of these problems, but in this case, we are, and that is why I added them together. Do you see the reason WHY these two equations can be added and the benefit that comes along with that process? Therefore:
x + y = 41 Now substitute your x value.
24 + y = 41
y = 41-24
y = 17
The two values are now, 24 and 17
PROOF your work:
24 + 17 = 41 (First condition that the two numbers must equal or have a sum of 41). This condition is met.
24 - 17 = 7 (Second condition that the diffeence between the two is 7). This condition is met.
Therefore:
The the two numbers are 24 and 17.
x + y = 41 All we have done here is expressed what the problem is telling us, right?
The other condition, that the difference between the two is 7, needs to be met too.
Therefore:
x - y = 7
So, the two equations are:
x + y = 41
x - y = 7
Now add the two equations.
x + y = 41
x - y = 7
_________
2x = 48
x = 48/2 correct OR
x = 24
Please note: I am adding the two equations because I can ELIMINATE the y variable by doing so. We will not always be this fortunate with some of these problems, but in this case, we are, and that is why I added them together. Do you see the reason WHY these two equations can be added and the benefit that comes along with that process? Therefore:
x + y = 41 Now substitute your x value.
24 + y = 41
y = 41-24
y = 17
The two values are now, 24 and 17
PROOF your work:
24 + 17 = 41 (First condition that the two numbers must equal or have a sum of 41). This condition is met.
24 - 17 = 7 (Second condition that the diffeence between the two is 7). This condition is met.
Therefore:
The the two numbers are 24 and 17.
Mo, would you be so kind as to send me a follow up question letting me know that you understand the process I followed and how I arrived at my answer. Please ask anything you do not understand, because here is the thing: while I gave you the answer, it is much better if you know the why behind what I have done here. Have a great Sunday and short-week at school. I am glad to assist. ~Mark B.
