Problem of the Week

Updated at Aug 15, 2022 10:29 AM

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

How would you solve 20y+4+4y=22\frac{20}{y}+4+4y=22?

Check out the solution below!



20y+4+4y=22\frac{20}{y}+4+4y=22

1
Multiply both sides by yy.
20+4y+4y2=22y20+4y+4{y}^{2}=22y

2
Move all terms to one side.
20+4y+4y2−22y=020+4y+4{y}^{2}-22y=0

3
Simplify  20+4y+4y2−22y20+4y+4{y}^{2}-22y  to  20−18y+4y220-18y+4{y}^{2}.
20−18y+4y2=020-18y+4{y}^{2}=0

4
Factor out the common term 22.
2(10−9y+2y2)=02(10-9y+2{y}^{2})=0

5
Split the second term in 10−9y+2y210-9y+2{y}^{2} into two terms.
2(2y2−4y−5y+10)=02(2{y}^{2}-4y-5y+10)=0

6
Factor out common terms in the first two terms, then in the last two terms.
2(2y(y−2)−5(y−2))=02(2y(y-2)-5(y-2))=0

7
Factor out the common term y−2y-2.
2(y−2)(2y−5)=02(y-2)(2y-5)=0

8
Solve for yy.
y=2,52y=2,\frac{5}{2}

Done

Decimal Form: 2, 2.5
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