SOLUTION: The sun of two numbers is 51. twice the first plus 4 times the second is 128. what are the numbers?

Question 80684: The sun of two numbers is 51. twice the first plus 4 times the second is 128. what are the numbers?
Found 2 solutions by bucky, praseenakos@yahoo.com:
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Call the first number F and the second number S
.
The sum of the first number and the second number equals 51. In equation form this is:
.
F + S = 51
.
Then the problem says that twice the first (2*F) plus four times the second (4*S) equals 128.
In equation form this is:
.
2F + 4S = 128
.
So we now have a set of two equations:
.
F + S = 51
2F + 4S = 128
.
We can solve this set of equations by the process of variable elimination. One way is
to multiply the to equation (all terms on both sides) by -2 to get:
.
-2F - 2S = -102
2F + 4S = 128
.
Now add the two equations vertically. When you do, the -2F in the top equation cancels the
2F in the bottom equation. Continuing with the vertical addition you get:
.
2S = 26
.
Dividing both sides of this equation by 2 results in:
.
S = 13
.
Now return to the original first equation which said that the sum of the first and second
numbers is 51 ...
.
F + S = 51
.
Substitute 13 for S and this equation becomes:
.
F + 13 = 51
.
Solve for F by subtracting 13 from both sides:
.
F = 38
.
In summary, the two numbers are 13 and 38
.
We already know that 13 plus 38 equals 51 as required by the problem.
.
Then 2 times the first is 2 * 38 and that equals 76. Add to that 4 times 13 which is 52.
The result of 76 + 52 is 128 as was also required by the problem. The answer checks.
.
Hope this helps you to understand the problem.
.

Answer by praseenakos@yahoo.com(507) (Show Source): You can put this solution on YOUR website!
QUESTION:

Sum of two numbers is 51. twice the first plus 4 times the second is 128. what are the numbers?

ANSWER:

Given that,
Sum of two numbers is 51

Let us assume that first number is x.

Then we can take the second number as 51-x (because their sum is given as 51)

Twice the first = 2x

4 times the second = 4(51-x)

twice the first plus 4 times the second is 128 can be expresssed as,

2x + 4(51-x) = 128

Remove the parenthesis, then we have

2x + 4 * 51 + 4 * (-x) = 128

==> 2x + 204 - 4x = 128

==> 2x - 4x + 204 = 128

==> -2x + 204 = 128

Subtract 204 from both sides of the equation.

==> -2x + 204 - 204 = 128 - 204

==> -2x + 0 = -76

==> -2x = -76

Divide both sides of the expression by -2

==> -2x/-2 = -76/-2

==> x = 38.

That is the first number is 38

So the second number is 51 - x = 51 - 38 = 13.

To check youe answer, plugg these values in the expression, 2x + 4(51-x) = 128

Then we have 2*38 + 4(51-38) = 128

==> 76 + 4* 13 = 128

==> 76 + 52 = 128

That is 128 = 128....means the values satisfies the given condition.

So the first number is 38 and the second number is 13.

Hope you understood.

Regards.

Praseena.

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