To find the weeks during which the sales equal 61,950 items, we can solve the given equation for x. The equation is:
y = 18.1sin(pi*x/24) + 52.9
We want to find the value of x when y (weekly sales) is equal to 61,950. Rearranging the equation, we have:
61,950 = 18.1sin(pi*x/24) + 52.9
Now, let's solve this equation step-by-step to find the corresponding weeks:
Step 1: Subtract 52.9 from both sides of the equation
61,950 - 52.9 = 18.1sin(pi*x/24)
61,897.1 = 18.1sin(pi*x/24)
Step 2: Divide both sides of the equation by 18.1
(61,897.1) / 18.1 = sin(pi*x/24)
3,418.4 = sin(pi*x/24)
Step 3: Take the inverse sine (sin^(-1)) of both sides of the equation
sin^(-1)(3,418.4) = sin^(-1)(sin(pi*x/24))
x = (24/pi) * sin^(-1)(3,418.4)
Step 4: Calculate the value of x using a calculator
x ≈ 24.293
So, the value of x is approximately 24.293. However, since x represents the time in weeks, we need to round this value to the nearest whole number.
Therefore, the sales will be equal to 61,950 items approximately during week 24.