One system of equations would be
L = w+4
H = w-10
4H + 8(wL) = 1544
There is one viable solution; the width is 12, the length is 16, and the height is 2.
Using substitution with the system of equations, we have
4(w-10)+8(w(w+4))=1544
4w-40+8(w²+4w)=1544
4w-40+8w²+32w=1544
Combining like terms, we have
8w²+36w-40=1544
Factoring out a 4, we have
4(2w²+9w-10)=1544
Dividing both sides by 4 gives us
2w²+9w-10=386
Subtract 386 from both sides to get
2w²+9w-396=0
Using the quadratic formula, we have
Since a negative width makes no sense, we know that w=12.
This means L=w+4=12+4=16 and H=w-10=12-10=2
L = w+4
H = w-10
4H + 8(wL) = 1544
There is one viable solution; the width is 12, the length is 16, and the height is 2.
Using substitution with the system of equations, we have
4(w-10)+8(w(w+4))=1544
4w-40+8(w²+4w)=1544
4w-40+8w²+32w=1544
Combining like terms, we have
8w²+36w-40=1544
Factoring out a 4, we have
4(2w²+9w-10)=1544
Dividing both sides by 4 gives us
2w²+9w-10=386
Subtract 386 from both sides to get
2w²+9w-396=0
Using the quadratic formula, we have
Since a negative width makes no sense, we know that w=12.
This means L=w+4=12+4=16 and H=w-10=12-10=2