# 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 $$\frac{20}{y}+4+4y=22$$?

Check out the solution below!

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

 1 Multiply both sides by $$y$$.$20+4y+4{y}^{2}=22y$2 Move all terms to one side.$20+4y+4{y}^{2}-22y=0$3 Simplify  $$20+4y+4{y}^{2}-22y$$  to  $$20-18y+4{y}^{2}$$.$20-18y+4{y}^{2}=0$4 Factor out the common term $$2$$.$2(10-9y+2{y}^{2})=0$5 Split the second term in $$10-9y+2{y}^{2}$$ into two terms.1 Multiply the coefficient of the first term by the constant term.$2\times 10=20$2 Ask: Which two numbers add up to $$-9$$ and multiply to $$20$$?$$-4$$ and $$-5$$3 Split $$-9y$$ as the sum of $$-4y$$ and $$-5y$$.$2{y}^{2}-4y-5y+10$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$2(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))=0$7 Factor out the common term $$y-2$$.$2(y-2)(2y-5)=0$8 Solve for $$y$$.1 Ask: When will $$(y-2)(2y-5)$$ equal zero?When $$y-2=0$$ or $$2y-5=0$$2 Solve each of the 2 equations above.$y=2,\frac{5}{2}$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$y=2,\frac{5}{2}$Done Decimal Form: 2, 2.5y=2,5/2