Question

HELP PLEASE!

HAIR BUNDLES: B'UNIQUE Hair Salon owner buys seven hundred bags of a brand of synthetic hair bundles and four hundred bags of a brand of natural hair bundles for her Forestville and Largo locations to get ready to welcome back their clients for her reopening this weekend. The Forestville location receives three hundred bags of synthetic hair bundles and two hundred and fifty bags of natural hair bundles for a total retail value of twenty-three thousand, six hundred dollars. The Largo location receives four hundred bags of a brand of synthetic hair bundles and one hundred and fifty bags of a brand of natural hair bundles for a total retail value of twenty-four thousand, five hundred dollars. What is the retail value of one bag of a synthetic hair bundle and one bag of a natural hair bundle. In your answer, write a system of equations of how you would determine your answer. Provide evidence of your calculations and answer your result in a complete sentence.

Answer 1

The retail value of one bag of one bag of a synthetic hair bundle is $47 and the retail value of a bag of natural hair bundle is $38

Explanation:

The given information are;

The number of bags of synthetic hair bundles the owner buys = 700

The number of bags of natural hair bundles the owner buys = 400

The number of synthetic hair bundles the Forestville location receives = 300

The number of natural hair bundles the Forestville location receives = 250

The total retail value of the hair bundles the Forestville location receives = $23,600

The number of synthetic hair bundles the Largo location receives = 400

The number of natural hair bundles the Forestville location receives = 150

The total retail value of the hair bundles the Largo location receives = $24,500

Let the price of a bag of synthetic hair bundle = x

Let the price of a bag of natural hair bundle = y

∴ 300·x + 250·y = $23,600...(1)

400·x + 150·y = $24,500...(2)

Making y the subject of the formula in both equations gives;

For equation (1)

y = 23,600/250 - 300/250·x = 94.4 - 1.2·x

y = 94.4 - 1.2·x

For equation (2)

400·x + 150·y = 24,500

y = 24,500/150 - 400/150·x = 490/3 - 8/3·x

y = 490/3 - 8/3·x

Finding the common solution gives;

490/3 - 8/3·x = 94.4 - 1.2·x

490/3 - 94.4 = 8/3·x - 1.2·x

1034/15 = 22/15·x

x = 1034/15/(22/15) = 47

x = 47

∴ The price of a bag of synthetic hair bundle = x = $47

The price of a bag of synthetic hair bundle = $47

y = 490/3 - 8/3·x = 490/3 - 8/3 × 47 = 38

y = 38

The price of a bag of natural hair bundle = y = $38

The price of a bag of natural hair bundle = $38.

Therefore, the retail value of one bag of one bag of a synthetic hair bundle is $47 and the retail value of a bag of natural hair bundle is $38.