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morpeh [17]
3 years ago
7

how do I set up this word problem: I have 88 pieces of gum, I gave 4 pieces each to all my class mates, I have 8 pieces left, ho

w many people are in my class.
Mathematics
1 answer:
NeTakaya3 years ago
3 0
There are 20 people in the class room.

One way I set this word problem up is by using the equation 88-4x=8. X would stand for the amount of classmates in the class, 88 would stand for your total pieces of gum and 8 would stand for the remaining pieces left.

With the equation 88-4x=8 you want to subtract 88 from both sides to get the equation -4x=-80. Last you want to isolate x by dividing -4 on both sides to finally get x=20. 20 people in the class room.
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\large\boxed{\bold{NO\ REAL\ SOLUTIONS}}\\\boxed{x=4-2i,\ x=4+2i}

Step-by-step explanation:

Domain:\\c-4\neq0\ \wedge\ c-5\neq0\Rightarrow c\neq4\ \wedge\ c\neq5\\\\\dfrac{c}{c-5}=\dfrac{4}{c-4}\qquad\text{cross multiply}\\\\c(c-4)=4(c-5)\qquad\text{use the distributive property}\\\\c^2-4c=4c-20\qquad\text{subtract}\ 4c\ \text{from both sides}\\\\c^2-8c=-20\qquad\text{add 20 to both sides}\\\\c^2-8c+20=0\qquad\text{use the quadratic formula}

\text{for}\ ax^2+bx+c=0\\\\\text{if}\ b^2-4ac0,\ \text{then the equation has two solutions}\ x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}

x^2-8x+20=0\\\\a=1,\ b=-8,\ c=20\\\\b^2-4ac=(-8)^2-4(1)(20)=64-80=-16

\text{In the set of complex numbers:}\\\\i=\sqrt{-1}\\\\\text{therefore}\ \sqrt{b^2-4ac}=\sqrt{-16}=\sqrt{(16)(-1)}=\sqrt{16}\cdot\sqrt{-1}=4i\\\\x=\dfrac{-(-8)\pm4i}{2(1)}=\dfrac{8\pm4i}{2}=\dfrac{8}{2}\pm\dfrac{4i}{2}=4\pm2i

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