Question

164 is 184% of what number?

72 is 0.04% of what number?

please include proof

Answer 1

164 is 184% of 89.13

Answer 2

`\huge\boxed{89(3)/(23)\approx 89.13}\\\boxed{180,000}`

Explanation:

`\begin{array}{ccc}164&-&184\%\\x&-&100\%\end{array}\qquad\text{cross multiply}\\\\(184)(x)=(164)(100)\qquad|\text{divide both sides by 184}\\\\x=(16400)/(184)\\\\x=(16400:8)/(184:8)\\\\x=(2050)/(23)\\\\x=89(3)/(23)\approx 89.13`

`\begin{array}{ccc}72&-&0.04\%\\y&-&100\%\end{array}\qquad|\text{cross multiply}\\\\(0.04)(y)=(72)(100)\qquad|\text{divide both sides by }0.04\\\\y=(7200)/(0.04)\\\\y=180,000`