Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
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Chapter 24, Problem 26A
To determine

The amount of carbon needed to produce 2.60 tons of carbon steel required in the production of each type of tool.

Expert Solution & Answer
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Answer to Problem 26A

  59.8 pounds of carbon is required to make twist drill.

  39 pounds of carbon is required to make wrench.

  54.6 pounds of carbon is required to make threading die.

  65 pounds of carbon is required to make ordinary file.

  49.4 pounds of carbon is required to make Machinist's hammer.

  44.2 pounds of carbon is required to make Chuck jaw.

Explanation of Solution

Given information:

Below table is given for amount of carbon needed for different tool. Amount of carbon steel is 2.60 tons.

  Mathematics For Machine Technology, Chapter 24, Problem 26A

Calculation:

As per the given information amount of carbon steel is 2.60 tons.

Need to find the required percentage of carbon for different tool.

  1.Twist drill :

As we know the proportion to find percentage is given as

  PB=R100   where, P=percentage, B= base and R=rate

Here, amount of carbon steel will be base B=2.60 tons, percent of carbon in carbon steel is 1.15% i.e. R=1.15.

Putting these value in standard proportion,

  PB=R100P2.60=1.15100                           {Put B=2.60 and R=1.15}Applying cross multiplication,100P=1.15×2.60P=1.15×2.60100P=0.0299 tonsP=0.0299×2000                  {Since, 1 ton=2000 pound}P=59.8 pounds.

Hence, 59.8 pounds of carbon is required to make twist drill.

  2.Wrench :

As we know the proportion to find percentage is given as

  PB=R100   where, P=percentage, B= base and R=rate

Here, amount of carbon steel will be base B=2.60 tons, percent of carbon in carbon steel is 0.75% i.e. R=0.75.

Putting these value in standard proportion,

  PB=R100P2.60=0.75100                           {Put B=2.60 and R=0.75}Applying cross multiplication,100P=0.75×2.60P=0.75×2.60100P=0.0195 tonsP=0.0195×2000                  {Since, 1 ton=2000 pound}P=39 pounds.

Hence, 39 pounds of carbon is required to make wrench.

  3.Threading die :

As we know the proportion to find percentage is given as

  PB=R100   where, P=percentage, B= base and R=rate

Here, amount of carbon steel will be base B=2.60 tons, percent of carbon in carbon steel is 1.05% i.e. R=1.05.

Putting these value in standard proportion,

  PB=R100P2.60=1.05100                           {Put B=2.60 and R=1.05}Applying cross multiplication,100P=1.05×2.60P=1.05×2.60100P=0.0273 tonsP=0.0273×2000                  {Since, 1 ton=2000 pound}P=54.6 pounds.

Hence, 54.6 pounds of carbon is required to make threading die.

  4.Ordinary file :

As we know the proportion to find percentage is given as

  PB=R100   where, P=percentage, B= base and R=rate

Here, amount of carbon steel will be base B=2.60 tons, percent of carbon in carbon steel is 1.25% i.e. R=1.25.

Putting these value in standard proportion,

  PB=R100P2.60=1.25100                           {Put B=2.60 and R=1.25}Applying cross multiplication,100P=1.25×2.60P=1.25×2.60100P=0.0325 tonsP=0.0325×2000                  {Since, 1 ton=2000 pound}P=65 pounds.

Hence, 65 pounds of carbon is required to make ordinary file.

  5.Machinist's hammer :

As we know the proportion to find percentage is given as

  PB=R100   where, P=percentage, B= base and R=rate

Here, amount of carbon steel will be base B=2.60 tons, percent of carbon in carbon steel is 0.95% i.e. R=0.95.

Putting these value in standard proportion,

  PB=R100P2.60=0.95100                           {Put B=2.60 and R=0.95}Applying cross multiplication,100P=0.95×2.60P=0.95×2.60100P=0.0247 tonsP=0.0247×2000                  {Since, 1 ton=2000 pound}P=49.4 pounds.

Hence, 49.4 pounds of carbon is required to make Machinist's hammer.

  6.Chuck jaw :

As we know the proportion to find percentage is given as

  PB=R100   where, P=percentage, B= base and R=rate

Here, amount of carbon steel will be base B=2.60 tons, percent of carbon in carbon steel is 0.85% i.e. R=0.85.

Putting these value in standard proportion,

  PB=R100P2.60=0.85100                           {Put B=2.60 and R=0.85}Applying cross multiplication,100P=0.85×2.60P=0.85×2.60100P=0.0221 tonsP=0.0221×2000                  {Since, 1 ton=2000 pound}P=44.2 pounds.

Hence, 44.2 pounds of carbon is required to make Chuck jaw.

Therefore,

  59.8 pounds of carbon is required to make twist drill.

  39 pounds of carbon is required to make wrench.

  54.6 pounds of carbon is required to make threading die.

  65 pounds of carbon is required to make ordinary file.

  49.4 pounds of carbon is required to make Machinist's hammer.

  44.2 pounds of carbon is required to make Chuck jaw.

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Chapter 24 Solutions

Mathematics For Machine Technology

Ch. 24 - Finding Percentage, Percent, and Base in Practical...Ch. 24 - Finding Percentage, Percent, and Base in Practical...Ch. 24 - Finding Percentage, Percent, and Base in Practical...Ch. 24 - Finding Percentage, Percent, and Base in Practical...Ch. 24 - Finding Percentage, Percent, and Base in Practical...Ch. 24 - Finding Percentage, Percent, and Base in Practical...Ch. 24 - Prob. 17ACh. 24 - Finding Percentage, Percent, and Base in Practical...Ch. 24 - Finding Percentage, Percent, and Base in Practical...Ch. 24 - Finding Percentage, Percent, and Base in Practical...Ch. 24 - Prob. 21ACh. 24 - Prob. 22ACh. 24 - Finding Percentage, Percent, and Base in Practical...Ch. 24 - Finding Percentage, Percent, and Base in Practical...Ch. 24 - Prob. 25ACh. 24 - Prob. 26ACh. 24 - Finding Percentage, Percent, and Base in Practical...Ch. 24 - Finding Percentage, Percent, and Base in Practical...Ch. 24 - Finding Percentage, Percent, and Base in Practical...Ch. 24 - Finding Percentage, Percent, and Base in Practical...Ch. 24 - Prob. 31ACh. 24 - A manufacturer estimates that 15,500 pieces per...Ch. 24 - The average percent defective product of a...Ch. 24 - Prob. 34ACh. 24 - Prob. 35ACh. 24 - The cost of one dozen cutters is listed as $525. A...Ch. 24 - A manufacturer's production this week is 3620...Ch. 24 - Two machines are used to produce the same product....Ch. 24 - Allowing for scrap, a firm produced 1890 pieces....Ch. 24 - A manufacturing company receives $122,000 upon the...Ch. 24 - Prob. 41A
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