Question

Suppose that y varies directly with x, and y=15 when x=24. Write a direct variation equation that relates x and y. Find y when x=3

Answer 1

Answer:

$y=\frac{5}{8}x$

$y=\frac{15}{8}$, when $x=3$.

Step-by-step explanation:

We have been given that  y varies directly with x, and $y=15$ when $x=24$.

We know that two direct proportional quantities are in form $y=kx$, where k is constant of proportionality.

Let us find constant of proportionality by substituting $y=15$ and $x=24$ in above equation.

$15=k*24$

$\frac{15}{24}=\frac{k*24}{24}$

$\frac{3*5}{3*8}=k$

$\frac{5}{8}=k$

Therefore, our required equation would be $y=\frac{5}{8}x$.

Let us substitute $x=3$ in the equation.

$y=\frac{5}{8}(3)$

$y=\frac{15}{8}$

Therefore, the value of y is $\frac{15}{8}$.

Answer 2

Just set up a proportion with the original numbers and then the numbers you want to find like so: (x1/y1)=(x2/y2) and since you want to find the second y value, just leave y as a variable like so: (15/24)=(3/y) after this just cross multiply and get the answer: 15y=72.....y=4.8