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german
2 years ago
14

Kate used 555 grams of wool to knit a sweater, a hat, and a scarf. She used 5 times fewer grams for the hat than for the sweater

. She used 5 grams more for the hat than for the scarf. How many grams of wool did she use to knit each item?
Mathematics
1 answer:
elena55 [62]2 years ago
3 0

Answer:

Sweater =400 grams

Hat =80 grams

Scarf =75 grams

Step-by-step explanation:

The amount of wool used to make a sweater, a hat and a scarf=555 grams

Let the amount of wool used to make a sweater be = x

The amount of wool for the sweater =x/5

The amount of wool used for the scarf=x/5 -5

Total amount of wool used = x+(x/5)+(x/5-5)

x+x/5 +x/5-5=555

Multiply all through by the LCM 5

5x+x+x-25=2775

7x=2800

x=400

Sweater =400 grams

Hat=400/5=80 grams

Scarf =400/5 -5=75 grams

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Step-by-step explanation:

The given objective function is C = 60x + 85y

To check that which ordered pair is minimizing the objective function-we will substitute all the ordered pair one by one in the given function and we will calculate the value of C. The ordered pair which will give the minimum value will be the answer.

For (0, 160)

C=60\times 0+85\times 160=13600

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For (80, 50)

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Hence the ordered pair which minimizes the objective function is (80, 50)




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