the areas of the three non parallel face of right rectangular prism are in the ratio 15:9:4 and its volume is 300.determine the lengths of its sides.
A group of 50 people go to the candy store to buy candy bars. Each
person buys at least one bar. The store sells two types of candy bars, Sweet
and Tasty. If 45 people buy both types of Candy Bars, and 47 people buy
at least one Sweet bar each, how many people bought only Tasty candy
bars?
To find the lengths of the sides of the right rectangular prism, we need to use the given information about the ratios of the areas of its three non-parallel faces and its volume.
Let's denote the lengths of the sides of the prism as length (L), width (W), and height (H).
We are given that the areas of the three faces are in the ratio 15:9:4. Let's call these areas A1, A2, and A3, respectively.
Based on the given information, we can set up the following equations:
A1 : A2 : A3 = 15 : 9 : 4
Since the areas of the faces of a rectangular prism can be calculated as:
A1 = LW (area of face with length and width)
A2 = LH (area of face with length and height)
A3 = WH (area of face with width and height)
Now, let's substitute these equations into the ratio equation:
LW : LH : WH = 15 : 9 : 4
We know that the volume (V) of a rectangular prism can be calculated as:
V = LWH
We are given that the volume is 300, so we can substitute this into the above equation:
300 = LWH
Now we have a system of two equations. We can solve these equations simultaneously to find the values of L, W, and H.
To do this, we can use substitution or elimination method.
Let's use the substitution method:
From A1 : A2 : A3 = 15 : 9 : 4, we can rewrite the ratio equation:
LW : LH : WH = 15 : 9 : 4
Dividing each term by W, we get:
L : H : (H/W) = 15/W : 9/W : 4/W
Simplifying further, we have:
L : H : (H/W) = 15W/W : 9W/W : 4W/W
L : H : (H/W) = 15 : 9 : 4
Now, we can substitute (H/W) with a common variable, let's call it 'x':
L : H : x = 15 : 9 : 4
Now, using the volume equation: 300 = LWH, we can substitute L and H in terms of x:
L = 15x
H = 9x
Substituting these values into the volume equation:
300 = (15x)(9x)W
Simplifying:
300 = 135x^2W
To find the value of W, we need more information. The problem does not give any constraints or additional equations that allow us to solve for W. Therefore, we cannot determine the lengths of the sides of the right rectangular prism with the given information.