a sign says that the price marked on all music equipment is 30% off the original price you buy an electric guitar for sale price
1 answer:
The original price is $450.
<u>Step-by-step explanation:</u>
Step 1:
Given details, Discount%, D% = 30 and Selling Price, SP = $315
Step 2:
Write down formula for calculating the Original Price
Selling Price (SP) = Original Price (OP) - Discount (D)
Discount (D) = Original Price (OP) * (D%/100)
Step 3:
Substitute given values in the formula
315 = OP - D
D =
D = 0.3 OP
Step 4:
Substitute value of D in the first formula
315 = OP - 0.3 OP
315 = OP (1 - 0.3) = 0.7 OP
Original Price, OP = 315/0.7 = $450
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Answer: (A)
(B) Length varies between 1 and 150
(C) Largest area is 22500ft²
Step-by-step explanation: Suppose length is l and width is w.
The rectangular garden has perimeter of 600ft, which is mathematically represented as
Area of a rectangle is calculated as
Now, we have a system of equations:
Isolate w, so we have l:
w = 300 - l
Substitute in the area equation:
A = l(300 - l)
A = 300l - l²
(A) <u>Function of area in terms of length is given by </u><u>A = 300l - l²</u>
(B) The practical domain for this function is values between 1 and 150.
(C) For the largest area, we need to determine the largest garden possible. For that, we take first derivative of the function:
A' = 300 - 2l
Find the values of l when A'=0:
300 - 2l = 0
2l = 300
l = 150
Replace l in the equation:
w = 300 - 150
w = 150
Now, calculate the largest area:
A = 150*150
A = 22500
<u>The largest area the fence can enclose is </u><u>22500ft².</u>