Question

The actual length of a desk is 58 1/2 inches.Margaret estimates the length of the desk and find her percent erro to be less than 5%. Enter your answer as decimals or mixed numbers in simplest form by filling in the box.Margaret’s estimated length is between ( ) inches and ( ) inches.

Answer 1

Since it's been given that the percent error is less than 5%, the estimated length will be:

A.) Minimum : -5% of 58 1/2 inches

`\text{ 58 }(1)/(2)\text{ x }\frac{100\text{ - 5}}{100}\text{ = }\frac{116\text{ + 1}}{\text{ 2}}\text{ x }\frac{\text{ 95}}{\text{ 100}}`
`\text{ = }\frac{\text{ 117}}{\text{ 2}}\text{ x }\frac{\text{ 95}}{\text{ 100}}\text{ = }\frac{\text{ 11,115}}{\text{ 200}}`
`\text{ = 55.575 or 55}(23)/(40)\text{ inches}`

B.) Maximum : +5% of 58 1/2 inches

`\text{ 58}(1)/(2)\text{ x }\frac{\text{ 100 + 5}}{\text{ 100}}\text{ = }\frac{\text{ 117}}{2}\text{ x }\frac{105}{\text{ 100}}`
`\text{ =}\frac{12,\text{ 285}}{200}`
`\text{ = 61.425 or 61}(17)/(40)\text{ inches}`

Therefore, Margarets's esitmated length is between 55 23/40 inches and 61 17/40 inches.