To solve for the following proportion, you could use equivalent ratios, divide out the known ratio, or use cross products. Choose one of these methods to solve for t. Show your work and explain why you chose that method.
eighteen over five equals four over t.
18/5 = 4/t
cross-multiply:
18t = 20
t = 10/9
To solve for t in the proportion 18/5 = 4/t, you can use the method of cross products.
First, let's understand why we chose the method of cross products. In this method, we multiply the numerator of one ratio with the denominator of the other ratio to find equal products. This method is particularly useful when dealing with proportions because it allows us to find the missing value (in this case, t) by comparing the products of the ratios.
Now, let's apply the method:
Using cross products, we can say that the product of the numerator of the first ratio (18) and the denominator of the second ratio (t) is equal to the product of the denominator of the first ratio (5) and the numerator of the second ratio (4).
So, we have: 18 * t = 5 * 4
Simplifying this equation, we get:
18t = 20
To solve for t, we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 18:
(18t)/18 = 20/18
Simplifying further, we find:
t = 20/18
That is our final answer.
In summary, we chose to use the method of cross products to solve for t because it is a reliable approach for solving proportions. By applying cross products and algebraic manipulation, we found the value of t to be 20/18.