The sum of two numbers is 148 and their difference is 16. What are the numbers?
2007-01-29 10:27:37 · 7 answers · asked by larrylnguyen 1 in Science & Mathematics ➔ Mathematics
*You have two equations:
1. x + y = 148
2. x - y = 16
*The "x" & "y" variable represent unknown values/numbers.
First: let's solve for "x" in 2nd equation (you can solve for "x" or "y" in either equation) > add "y" to both sides...
2. x - y + y = 16 + y
x = 16 + y
Sec: replace "16 + y" with the y-variable in the 1st equation...
1. 16 + y + y = 148
16 + 2y = 148
*Subtract "16" from both sides...
16 - 16 + 2y = 148 - 16
2y = 132
*Isolate "x" on one side > divide both terms by "2"...
2y/2 = 132/2
y = 66
Third: replace "66" with the y-variable in the 2nd equation...
2. x - 66 = 16
*Add "66" to both sides...
x - 66 + 66 = 16 + 66
x = 82
Solution: (82, 66)
2007-01-29 11:58:57 · answer #1 · answered by ♪♥Annie♥♪ 6 · 2⤊ 0⤋
The sum means add. The difference means you subtract.
So, x + y = 148
x - y = 16
Solve either by ELIMINATION.
Add the above equation and you eliminate y. You get
2x = 164
Divide both sides by 2
x = 82 then solve for y in any of the given equation.
Use x+y = 148, then
82 + y = 148
y = 66
Or, by SUBSTITUTION, as in the response of the first answerer.
Choose whatever method you are comfortable with, but usually it helps to look at the equations first before even jumping in. In this case, ELIMINATION is more efficient.The y's have the same coefficients and opposite signs already.
2007-01-29 18:37:34 · answer #2 · answered by Aldo 5 · 2⤊ 0⤋
x-y=16 ..... x=16+y
x+y=148..... 16+y+y=148
2y+16=148
2y= 148-16
2y= 132
y=132/2
y=66
x= 16+y
x= 16+66
x= 82
2007-01-29 18:31:09 · answer #3 · answered by ? 5 · 2⤊ 0⤋
x + y = 148 (the sum is 148)
x - y = 16 (the difference is 16)
Add the above equations
2x = 164
Divide both sides by 2
x = 82
SInce x+y = 148, then
82 + y = 148
y = 66
82 and 66 are the numbers.
You can easily check your answer.
Just check their sum and difference.
2007-01-29 18:31:56 · answer #4 · answered by MsMath 7 · 4⤊ 0⤋
x + y = 148 (given)
x - y = 16 (also given)
So add the system of equations:
(x + y) + (x - y) = 148 + 16
2x = 164
x = 82
Then plug that into one of the equations:
82 - y = 16
82 = 16 + y
y = 66
2007-01-29 18:34:00 · answer #5 · answered by J 2 · 2⤊ 0⤋
148 devided by 2 = 74
74 + half of 16 = 82
74 - half of 16 = 66
66 + 82 = 148
2007-01-29 18:33:25 · answer #6 · answered by mrzwink 7 · 2⤊ 0⤋
82
66
82+66=148
82-66=16
2007-01-29 18:46:51 · answer #7 · answered by Anonymous · 2⤊ 1⤋