# A clothing manufacturer uses the model a=f+4−−−−√−36−f−−−−−√ to estimate the amount of fabric to order from a mill. In the formula, a is the

Question

A clothing manufacturer uses the model a=f+4−−−−√−36−f−−−−−√ to estimate the amount of fabric to order from a mill. In the formula, a is the number of apparel items (in hundreds) and f is the number of units of fabric needed. If 4 apparel items will be manufactured, how many units of fabric should be ordered?

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1 year 2021-09-03T10:19:36+00:00 1 Answers 100 views 0

1. Questions:

A clothing manufacturer uses the model a = √(f + 4) – √(36 – f) to estimate the amount of fabric to order from a mill. In the formula, a is the number of apparel items (in hundreds) and f is the number of units of fabric needed. If 400 apparel items will be manufactured , how many units of fabric should be ordered?

32 units of fabrics

Step-by-step explanation:

Given

$$a = \sqrt{f + 4} – \sqrt{36 – f}$$

Required

Find f when a  = 4

Substitute 4 for a

$$4 = \sqrt{f + 4} – \sqrt{36 – f}$$

Rewrite as:

$$\sqrt{36 – f} + 4 = \sqrt{f + 4}$$

Square both sides

$$(\sqrt{36 – f} + 4)^2 = (\sqrt{f + 4})^2$$

$$(\sqrt{36 – f} + 4)^2 = f + 4$$

$$36 – f + 8\sqrt{36 – f} + 16 = f + 4$$

Collect Like Terms

$$8\sqrt{36 – f}= f +f+ 4 – 36 -16$$

$$8\sqrt{36 – f}= 2f -48$$

Divide through by 2

$$4\sqrt{36 – f}= f -24$$

Square both sides

$$16(36-f) = (f – 24)^2$$

$$16(36-f) = f^2 – 48f + 576$$

$$576-16f = f^2 – 48f + 576$$

$$-16f = f^2 – 48f$$

Collect like terms

$$f^2 – 48f + 16f = 0$$

$$f^2 -32f = 0$$

Factorize

$$f(f – 32) = 0$$

$$f = 0$$ or $$f = 32$$

f can not be 0 because some units must be ordered.

So, f = 32