Question 478004: The sum of two numbers is 248. Their difference is 64. find the number.
Found 3 solutions by Theo, ikleyn, greenestamps:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! x + y = 264
x - y = 64
use first equation to solve for y and then substitute that value for y in the second equation.
x + y = 264
y = 264 - x
substitute for y in the second equation to get:
x - (264 - x) = 64
remove parentheses to get:
x - 264 + x = 64
combine like terms to get:
2x - 264 = 64
add 264 to both sides of the equation to get:
2x = 328
divide both sides of the equation by 2 to get:
x = 164
substitute for x in the first equation to get:
x + y = 264 becomes:
164 + y = 264
subtract 164 from both sides of the equation to get:
y = 264 - 164 = 100
you have:
x = 164
y = 100
substitute in both original equations to confirm the answer is good.
first equation is x + y = 264
substituting for x and y gets:
164 + 100 = 264 which is true
second equation is x - y = 64
substituting for x and y gets:
164 - 100 = 64
both original equations are true confirming the value of 164 for x and 100 for y are good.
Answer by ikleyn(52873)  (Show Source):
You can put this solution on YOUR website! .
The sum of two numbers is 248. Their difference is 64. find the number.
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The solution to this problem in the post by @Theo, giving the answer x = 164, y = 100, is incorrect.
It does not satisfy the condition x+y = 248.
I came to bring a correct solution.
Let x be the greater number, y be the smaller number.
We have then these two equations
x + y = 248, (1)
x - y = 64. (2)
You can solve this system of two linear equations by the Substitution method
or by the Elimination method, on your choice.
Let' solve by the Elimination method.
Add equations (1) and (2). The terms with 'y' will annihilate,
and you will get
2x = 248 + 64 = 312,
x = 312/2 = 156.
Now find 'y' from equation (1)
y = 248 - x = 248 - 156 = 184.
ANSWER. x = 156, y = 92.
CHECK. x + y = 156 + 92 = 248 (correct). x - y = 156 - 92 = 64 (correct).
Solved correctly.
Answer by greenestamps(13208)  (Show Source):
You can put this solution on YOUR website!
Tutor @ikleyn has provided a response showing a standard formal algebraic solution, forming two equations directly from the given information and solving the pair of equations using elimination.
Repeated here by way of demonstration....
x+y = 248 [the sum of the two numbers is 248]
x-y = 64 [the difference of the two numbers is 64]
2x = 312 [by adding the two equations]
x = 156
y = 248-156 = 92
ANSWERS: 156 and 92
With a bit of practice, you can get the solution more quickly using exactly the same calculations but without the formal algebra.
The idea is this: you start with the first number and add the second, getting 248; and you start with the same first number and subtract the second, getting 64. If you picture that on a number line, that means the first number is exactly halfway between 248 and 64. So....
The first number is (248+64)/2 = 312/2 = 156
The second number is 248-156 = 92
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