Answer:
Volume = 0.84 in^3
Explanation:
Let W and L be the Width and Length of the brick. Let H be the height.
We are told that "The width of a brick is half the length," which we can write as:
W = (1/2)L
We also learn that the length, L, is 2 inches less than 8 times the height. This can be written as:
L = 8*H - 2"
We finally learn that "the sum of the three dimensions is 26.25 inches," which converts into the following:
W + L + H = 26.25"
We want the volume: Volume = W*L*H
We'll need to use substitution to eliminate two of the variables to get a start on the other two unknowns. We can see from the two first equations that both contain the variable L. Let's rearrange them to find how the second variable is a function of L:
W = (1/2)L (already arranged for W =)
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L = 8*H - 2"
8*H = L + 2"
H = (L + 2")/8
==
Now use these two definitions of W and H in the third equation:
W + L + H = 26.25"
(1/2)L + L + ((L + 2")/8) = 26.25"
4L + 8L + L+ 2' = 26.25" [Multiply both sides by 8]
13L = 24.25"
L = 1.87"
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Since W = (1/2)L
W = (1/2)*(1.87")
W = 0.933"
Since H = (L + 2")/8
H = (1.87" + 2")/8
H = (3.87")/8
H = 0.484"
Volume = W*L*H
Volume = (0.933")*(1.87")*(0.484")
Volume = 0.84 in^3