Problems with Two Unknowns: Sum of 2 #'s is 105, smaller # is 5 less than larger #. How do I solve this?

Question

The question comes from my summer math packet. These questions as I remember seemed to stump me on the final.

"The sum of two numbers is 105. The smaller number is 5 less than the larger number. Find the numbers."

I set up:

X+Y=105
X-Y=5

I don't seem to get the right answer.

Answer 1

Your two equations are right. Now use the addition method.
Add the two equations.
X+Y=105
X-Y=5
2X = 110
X = 110/2
X = 55
Now replace X with 55 in one of the above equations and solve for Y
55 + Y = 105
Y = 105 - 55
Y = 50
Answer: The two numbers are 50 and 55.

Answer 2

Let's assume the larger number is X.
Therefore, the smaller number would be (X-5)

X + (X-5) = 105
2x -5 = 105
+5 +5
2x = 110
/2 /2
x=55

So, the two numbers are
x = 55
y (or x-5) is 50

Answer 3

X-y=5 so x= y+5

now substitute in for x ...

so the top equation becomes:

y+5+y=105 or :

2y + 5 = 105 so :
2y = 105 - 5 or 100
so y = 50 ...

Answer 4

smaller # is x
larger is y

x+y = 105

y-5 = x

so plug it in:

(y-5) + y = 105

2y - 5 = 105

2y = 110

y = 55

plug y into original equation for x : y-5 = x

55-5 =x

x = 50


check: 50 + 55 = 105!!!

tada!

Answer 5

X+Y=105
X-Y=5
.............
2X=110
X=110/2
X=55
X-Y=5
55-Y=5
Y=55-5
Y=50

Answer 6

x = 55
y = 50