Can some one help me out?

Question

The first number is 4 times larger than another number and the smaller number is decreased by 2. The result is 14 less than the larger number. What are the two numbers?

Please explain how you got the answer, this is not homework just something I came across.

Answer 1

x -2 = 4x -14
3x = 14 -2
x = 4
4x = 16

the two numbers are 4 and 16

Answer 2

Step 1: Name your variables.
Let f be the First number, and
let n be the other Number.

Step 2: Translate the verbal statements into equations.
"first number is 4 times larger than another number" becomes

f = 4 * n

"the smaller number is decreased by 2. The result is 14 less than the larger number"
becomes

n - 2 = f - 14

Here you have two equation with two unknowns.

Step three: Solve the linear system
You can solve it a number of ways. The easiest is substitution.

The hardest part was getting the second equation, because the problem was worded a little strangely.

Answer 3

OK, let's call the smaller number (before it's decreased) x.

The larger number is therefore 4x.

When the smaller number is decreased by 2, it becomes x-2.

We're told that x-2 is 14 less than the larger number, so:

x - 2 = 4x - 14

To solve this for x, we start by subtracting x from both sides:

x - 2 - x= 4x - 14 - x
-2 = 3x - 14

Then we add 14 to both sides:

-2 + 14 = 3x - 14 + 14
12 = 3x

Finally, we divide both sides by 3:

12/3 = 3x/3
4 = x

So our smaller number (before it's decreased) is 4. After it's decreased, it would then be 2. The larger number is 4 times the (original) smaller one, which makes it 16, and 2 is indeed 14 less than 16.

Hope that clears it up!

Answer 4

Let the two numbers be A and B

Then, A= 4B .................(1)
and B - 2 = A - 14.........(2)

Substitute for A into (2)
B -2 = 4B - 14
12 = 3B,
B = 4

Substitute for B into (1)
A = 4 x 4 = 16

Ans. The two numbers are A = 16 and B = 4

Answer 5

16 and 4, 4x4=16-2=14 in less then 16

Answer 6

You can solve the problem using one variable or two variables. Once you understand how to convert a word problem into algebra, and how to solve the algebra, it becomes easy for you. You enjoy solving problems.
So, three steps are involved.
1) Conversion word problem to mathematics.
2) solving the mathematical problem
3) interpretation of the results.
Understand the answers from other correspondents. Understand the methodology. Proceed to solve all problems. Practise makes one perfect.

Answer 7

TYPE the question correctly - I guess you got the punctuations in wrong place.

x = 4y
y-2 = x-14

y-2=4y-14
3y=12
y=4
x=16

Answer 8

sorry i stink at math.

Answer 9

yah, right