The value of y varies directly with x. When y = -12 1/2, x = 50. What is the value of y when x is 11 3/4, rounded to the nearest hundredths?
Can someone please show me how to solve this problem?
y = k x
-12.5 = 50 k
-25 = 100 k
k = -1/4
y = -x/4
y = - (47/4) / 4
= - 47/16
since y=kx, y/k = k is constant, so you want y such that
y/(11 3/4) = (-12 1/2)/50
y = -47/16
To solve this problem, we need to find the constant of proportionality between y and x. Let's call this constant "k". The direct variation equation is written as:
y = kx
To find the value of "k", we can use the given data point (y = -12 1/2 when x = 50). Plugging these values into the equation, we have:
-12 1/2 = k * 50
Now, let's solve for "k". To remove the fraction, we can rewrite -12 1/2 as -25/2. The equation becomes:
-25/2 = k * 50
To find "k", divide both sides of the equation by 50:
k = (-25/2) / 50
k = -25/100
k = -1/4
Now that we know the value of "k" is -1/4, we can use this constant of proportionality to find the value of y when x = 11 3/4.
Substituting the known values into the equation, we have:
y = (-1/4) * 11 3/4
To simplify this expression, we need to convert the mixed number into an improper fraction:
11 3/4 = (4 * 11 + 3) /4
= 47/4
Now, substitute this value into the equation:
y = (-1/4) * 47/4
y = (-1 * 47)/(4 * 4)
y = -47/16
To round this value to the nearest hundredths, we divide the numerator (-47) by the denominator (16):
-47 ÷ 16 ≈ -2.9375
Rounding to the nearest hundredths, we get:
y ≈ -2.94
Therefore, the value of y when x is 11 3/4, rounded to the nearest hundredths, is approximately -2.94.