Question

If y varies directly with x and y= 12 when x= 16, what is the value of x when y= 5?

Answer 1

Answer:

$x = 6 \frac{2}{3}$

Step-by-step explanation:

Since y varies directly with x,

y= kx, where k is a constant.

① Find the value of the constant k.

When y=12, x= 16,

12= k(16)

16k= 12

$k = \frac{12}{16} \\ k = \frac{3}{4}$

②Substitute the value of k back into the equation:

$y = \frac{3}{4} x$

③ Find value of x when y=5.

When y=5,

$5 = \frac{3}{4} x \\ x = 5 \div \frac{3}{4} \\ x = 5 \times \frac{4}{3} \\ x = \frac{20}{3} \\ x = 6 \frac{2}{3}$