Assuming that y varies directly as x, if x = 4 when y = 10, find x when y = 25

Answer 1

There are several approaches to this problem, but I would solve it with a proportion because I think it is the simplest way and because I like students to see the strength of proportions.

You are told that "y varies directly as x." That can be restated in several ways, but let's just say that it means that the ratio of x/y will always be the same, no matter the x or the y that you choose. Now it's time to look at the specific values for x and y that you have been given and set those up as a proportion, meaning to ratios or fractions set equal to one another.

x1 x2

----- = ------

y1 y2

By the way, you could set up such a proportion for any linear relationship, using ordered pairs that satisfy the equation for the given line. In this case, we're not going to worry about the equation for a line. We're just going to fill in the three values we have in the above proportion and solve for the one value we don't have.

4 x2

------ = -----

10 25

I will let you solve for x2, which is the value of x when y is 25. I recommend using cross-multiplication. Good luck!

Answer 2

Since y varies directly as x, we know we can multiply each x value by the same constant, k, to find the value of y. Or in other words, y = k * x. If x=4 when y=10, we have the equation 10 = k * 4. Solving for k by dividing both sides of the equation by 4, we get that k = 10/4 or 5/2 or 2.5 if you want to use a decimal. So the formula for this situation is y = 2.5x. That will let us find every pair of x and y values that have the same relationship shown in the equation. If y = 25, then 25 = 2.5x. Dividing both sides of the equation by 2.5 gives us a value for x of 10 when y is 25.