Question

Suppose y varies directly as x and y=3/4 when x=24. Write and solve a direct variation equation to find y when x=12.

Answer 1

By determining the constant of variation (k=1/32) from the given values, we derived the direct variation equation, y = (1/32)x. Using this equation, we calculated y to be 3/8 when x is 12.

Step-by-step explanation:

Given that y varies directly as x and that y=3/4 when x=24, we can find the constant of variation by using the formula y = kx, where k is the constant of variation. We solve for k by substituting the given values:

y = kx
3/4 = k(24)

Dividing both sides by 24 gives us:

k = (3/4) / 24
k = 1/32

Now that we have the constant of variation, the direct variation equation is y = (1/32)x. To find y when x=12, we substitute 12 for x:

y = (1/32)(12)
y = 12/32
y = 3/8

Therefore, when x=12, y equals 3/8.