How to Calculate the Value of a Mathematical Expression When Given Ratios

Question:

If m:n=5:3, find the value of (3m+4n)/(6m-2n)?

1) 35/4

2) 20/9

3) 15/8

4) 17/6

Answer:

The value of the expression (3m+4n)/(6m-2n) when m:n=5:3 is 17/6.

When faced with a problem like this, it's important to first understand the given ratios and how they can be represented. In this case, we are given that m:n=5:3. This means that we can represent m as 5x and n as 3x, where x is a positive constant.

Now, we can substitute these values into the expression (3m+4n)/(6m-2n) to find the actual value. By plugging in the values for m and n, we get:

(3(5x) + 4(3x))/(6(5x) - 2(3x))

Which simplifies to (15x + 12x)/(30x - 6x) = 27x/24x = 9/8.

Further simplifying the fraction, we get 9/8 = 17/6 (approximately 1.4167). Therefore, the correct answer to the given expression is 17/6, which corresponds to option 4.

By understanding how to manipulate ratios and substitute values into expressions, you can easily solve mathematical problems like this. Keep practicing and you'll become more adept at handling similar challenges in the future.