Simultaneous Equation Word Problem Example 1
Problem #60 p.498 of A Graphical Approach to College Algebra by Hornsby and Lial
Jose Ortega is a building contractor. If he hires 8 bricklayers 8 bricklayers and 2 roofers 2 roofers 2 roofers , his daily payroll is $960 $960 , while 10 bricklayers 10 bricklayers and 5 roofers 5 roofers 5 roofers require a daily payroll of $1500 $1500 What is the daily wage of a bricklayer and the daily wage of a roofer?
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Step 1 of the solution These problems are slightly different from previous ones in that the x variable and y variable count very similar things and are not related by cause and effect. A cause and effect relationship does exist between the counts of the two broadest categories of things mentioned in this problem. Both x and y are conversion factors (slopes) in the relationship between the two types of counting. Eventually, we will be separating the x related values into one row of the "rate" table and the y related values into another. However, we will begin by looking for the two broadest categories of things that are being counted in this problem. Can you see two different types of counts in the problem above? |
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After you find two different types of counts above, click on the button to the left to see if you were correct. |
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You were
asked to find the two general types of unit or counts that are referred to.
The answers are the number of employees and the amount of money paid to them.
You can see that these quantities are referred to in the questions below.
If you click on the colored words of the questions below, the corresponding
words and numbers will flash with the same color in the text of the problem.
Try clicking now.
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Step 2 of the solution Now that you have found the two general types of unit, employees and money, you must observe which of these two types has two more specific subtypes. Are there two more specific types of employee or are there two more specific types of money? |
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After you find two subtypes above, click on the button to the left to see if you were correct. |
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There
are two specific types of employee mentioned, the bricklayers and the roofers.
The first type is the bricklayers, referred to in the red question below.
The roofers are the employees referred to in the green question. When you
click on a question the corresponding words and numbers will flash the same
color in the text of the problem.
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Step 3 of the solution Now comes the big step, putting the results into a "rate" table. The table headings will be the usual: "the number of these for each one of those" times "the number of those" equals "the total number of these". "These" and "those" will refer to the general types of unit found in the first step. The new twist is that the table will have three rows. The first will be for the first specific type of employee. The unknown entry in that row we be our x variable. The unknown in the second row below it will be our y variable. We will be using numbers from the first payroll option only. In actually solving the problem, we would also have to make a second table for the second option. Each table represents one equation. You will eventually fill a number from the problem into the bottom right-hand entry of the table. Remember that each of the two entries above that in the right-hand column is simply the product of the other two entries in the same row. The equation comes entirely from the third column. We simply add the top two entries of the third column together and set the sum equal to the bottom entry. |
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After reading the above, click on the button to the left to fill in the table, including column headings. |
| The amount of for each | the number of | The total amount of | |
| Bricklayers | |||
| Roofers | |||
| Total |