Problem of the Week

Updated at May 6, 2019 4:09 PM

To get more practice in equation, we brought you this problem of the week:

How can we solve the equation 33−w+20w=52\frac{3}{3-w}+\frac{20}{w}=\frac{5}{2}?

Check out the solution below!



33−w+20w=52\frac{3}{3-w}+\frac{20}{w}=\frac{5}{2}

1
Multiply both sides by the Least Common Denominator: 2w(3−w)2w(3-w).
6w+40(3−w)=5w(3−w)6w+40(3-w)=5w(3-w)

2
Simplify.
−34w+120=15w−5w2-34w+120=15w-5{w}^{2}

3
Move all terms to one side.
34w−120+15w−5w2=034w-120+15w-5{w}^{2}=0

4
Simplify  34w−120+15w−5w234w-120+15w-5{w}^{2}  to  49w−120−5w249w-120-5{w}^{2}.
49w−120−5w2=049w-120-5{w}^{2}=0

5
Multiply both sides by −1-1.
5w2−49w+120=05{w}^{2}-49w+120=0

6
Split the second term in 5w2−49w+1205{w}^{2}-49w+120 into two terms.
5w2−24w−25w+120=05{w}^{2}-24w-25w+120=0

7
Factor out common terms in the first two terms, then in the last two terms.
w(5w−24)−5(5w−24)=0w(5w-24)-5(5w-24)=0

8
Factor out the common term 5w−245w-24.
(5w−24)(w−5)=0(5w-24)(w-5)=0

9
Solve for ww.
w=245,5w=\frac{24}{5},5

Done

Decimal Form: 4.8, 5
Cymath foriOSAndroid