Consider the numbers 1,2,3, and 5.
If the same numer is added to each of the numbers, it is found that the ratio of the first new number to the second is the same as the ratio of the third new number to the fourth. Find the number. Please help... I do not know how to set this up.
Heather
Let x be the number you want to find.
(x+1)/(x+2) = (x+3)/(x+5)
Multiply that out to get
x^2 + 6x + 5 = x^2 + 5x + 6
Cancel out the x^2 terms. Solve for x. Pretty easy.
To set up the equation, we need to analyze the given information.
Let's say the number we want to find is x.
According to the problem, if the same number is added to each of the given numbers (1, 2, 3, and 5), we get new numbers. Let's call these new numbers (x+1), (x+2), (x+3), and (x+5).
The problem states that the ratio of the first new number to the second is the same as the ratio of the third new number to the fourth.
This can be written as:
(x+1)/(x+2) = (x+3)/(x+5)
Now, we can solve this equation to find the value of x.
To do that, we can cross-multiply:
(x+1) * (x+5) = (x+3) * (x+2)
Expanding both sides of the equation:
(x^2 + 6x + 5) = (x^2 + 5x + 6)
Now, we can simplify the equation by canceling out the common term (x^2) on both sides:
6x + 5 = 5x + 6
Rearranging the equation:
6x - 5x = 6 - 5
x = 1
Therefore, the value of x is 1.