I need this question answered fully and competely. Sally purchases hardwood lumb

Question

I need this question answered fully and competely.

Sally purchases hardwood lumber for a custom furniture-building shop. She uses three suppliers, Northern Hardwoods, Mountain Top, and Spring Valley. Lumber is classified as either clear or has defects. Sally estimates that defects constitute 10% of the lumber pile. A recent analysis of the defect lumber pile showed that 30% came from Northern Hardwoods and 50% came from Mountain Top. Analysis of the clear pile indicates that 40% came from Northern and 40% came from Spring Valley. What is the percent of clear lumber from each of the three suppliers? What is the percent of lumber from each of the three suppliers?

Explanation / Answer

ans=

1. What is the percent of clear lumber from each of the three suppliers?

% of clear lumber of the whole pile = 100% - 10% = 90%

% of clear lumber from Northern Hardwoods = (40%)*(90%) = 36%

% of clear lumber from Spring Valley = (40%)*(90%) = 36%

% of clear lumber from Mountain Top (100% - (40% + 40%))*90% = 18%

2. What is the percent of lumber from each of the three suppliers?

Percentage of defective lumber from Spring Valley = 100% - (30% + 50%) = 20%

% of lumber from Northern Hardwoods = its (% defective lumber + % clear lumber) of the whole pile

= (30%)*(10%) + 32% = 3% + 32% = 35%

% of lumber from Mountain Top = its (% defective lumbers + % clear lumber) of the whole pile

= (50%)*(10%) + 16% = 5% + 16% = 21%

% of lumber from Spring Valley = its (% defective lumbers + % clear lumber) of the whole pile

= (10%)*(10%) + 32% = 1% + 32% = 33%

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