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Patio Furniture
publish date: 2024/04/23 21:01:39.781062 UTC
A production process applies several layers of a clear plastic coat to outdoor furniture to help protect it from the weather. If each protective coat is \(\frac{3}{32}\)-inch thick, how many applications will be needed to build up \(\frac38\) inch of clear finish?
Correct Answer
$4$
Explanation
In order to solve this problem, We divide the required coat thickness
Given:
- Thickness of each protective coat = \(\frac{3}{32}\) inch
- Total desired thickness = \(\frac38\) inch
To find the number of applications needed, we divide the total desired thickness by the thickness of each coat:
Number of applications = Total desired thickness \ Thickness of each coat
Number of applications = \(\frac38 ÷ \frac{3}{32}\)
When we divide fractions, we invert the divisor and multiply:
Number of applications = \( \frac38 \cdot \frac{32}{3} \)
When breaking the numbers into its factor we get = \( \frac{3}{8} \cdot \frac{4 \cdot 8}{3}\)
Apply the division and remove similar factors = \(\require{cancel} \frac{\cancel{3}^1}{\cancel{8}_1} \cdot \frac{4 \cdot \cancel{8}^1}{\cancel{3}_1} = \frac41 = 4\)
Number of applications = 4
Reference
Mathematics for college students