Problem of the Week

Updated at Oct 7, 2024 1:41 PM

For this week we've brought you this equation problem.

How would you solve 7+4w+5w=9747+4w+\frac{5}{w}=\frac{97}{4}?

Here are the steps:



7+4w+5w=9747+4w+\frac{5}{w}=\frac{97}{4}

1
Multiply both sides by 4w4w.
28w+16w2+20=97w28w+16{w}^{2}+20=97w

2
Move all terms to one side.
28w+16w2+20−97w=028w+16{w}^{2}+20-97w=0

3
Simplify  28w+16w2+20−97w28w+16{w}^{2}+20-97w  to  −69w+16w2+20-69w+16{w}^{2}+20.
−69w+16w2+20=0-69w+16{w}^{2}+20=0

4
Split the second term in −69w+16w2+20-69w+16{w}^{2}+20 into two terms.
16w2−5w−64w+20=016{w}^{2}-5w-64w+20=0

5
Factor out common terms in the first two terms, then in the last two terms.
w(16w−5)−4(16w−5)=0w(16w-5)-4(16w-5)=0

6
Factor out the common term 16w−516w-5.
(16w−5)(w−4)=0(16w-5)(w-4)=0

7
Solve for ww.
w=516,4w=\frac{5}{16},4

Done

Decimal Form: 0.3125, 4
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