Answer:
The largest number of pyramids she can make from 20 bars of chocolate is:
Step-by-step explanation:
Firstly, you must find the volume of the 20 bars of chocolate, remember that each bar contains 6 cubic inches of chocolate (6 in^3), so:
- Volume of the bars = 6 in^3 * 20
- <u>Volume of the bars = 120 in^3</u>
Now, you must find the volume of each pyramid, using the next formula:
- Volume of a pyramid = 1/3 B * h
Where:
<em>B = area of the square base.</em>
<em>h = height of the pyramid.</em>
How these values are given in the problem, we only replace the values in the formula:
- Area of a pyramid = 1/3 (1 in^2) * 2 in
- <u>Area of a pyramid = 2/3 in^3</u>
Finally, we divide the volume of the bars in the volume of each pyramid:
- Total number of pyramids = 120 in^3 / 2/3 in^3
- <u>Total number of pyramids = 180</u>
Answer: x = 5
Step-by-step explanation:
Want me to show this, or did you just want the answer?
The idea here is to combine the equations into one in only one variable. The last equation is in only x and z so lets sub out y in the second.
-x - y - z = -8
8 - x - z = y
Substitute y with (8 - x - z) into the next equation.
-4x + 4(8 - x - z) + 5z = 7
-4x + 32 - 4x - 4z + 5z = 7
-8x + 32 + z = 7
The variable z is easiest to get alone; use that as substitution in the last equation.
z = 7 + 8x - 32
z = 8x - 25
Substitute z with (8x - 25)
2x + 2(8x - 25) = 4
2x + 16x - 50 = 4
18x = 4 + 50
18x = 54
x = 3
So use x = 3 in that last equation to find z.
2(3) + 2z = 4
6 + 2z = 4
2z = 4 - 6
2z = -2
z = -1
Now, use both x = 3 and z = -1 to find the final variable y.
-3 - y - (-1) = -8
-3 - y + 1 = -8
-2 - y = -8
-y = -8 + 2
-y = -6
y = 6
Solutions x,y,z = ( 3, 6, -1)
