   Chapter 4.1, Problem 65E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

Pollution Joe Slo, a college sophomore, neglected to wash his dirty laundry for 6 weeks. By the end of that time, his roommate had had enough and tossed Joe's dirty socks and T-shirts into the trash, counting a total of 44 items. (A pair of dirty socks counts as one item.) The roommate noticed that there were three times as many pairs of dirty socks as T-shirts. How many of each item did he throw out?

To determine

To calculate: The number of items, dirty socks and T-shirts, Joe Slo’s roommate threw out in the trash, if Joe Slo, a college sophomore was not want to wash his dirty laundry for 6 weeks, so at the end of time, his roommate had enough dirty socks and T-shirts into the trash which was total of 44 items.

Explanation

Given Information:

Joe Slo, a college sophomore was not want to wash his dirty laundry for 6 weeks, so at the end of time, his roommate had enough dirty socks and T-shirts into the trash which was total of 44 items. A pair of socks considered as one item. The roommate of Joe Slo noticed that there were three times as many pairs of dirty socks as T-shirts.

Formula used:

Elimination method:

Step 1: Consider the linear equations in two variables.

Step 2: The equations are multiplied with suitable non-zero numbers to convert the coefficients to equals of opposite signs.

Step 3: The equations are combined to eliminate one variable, and the value of the other variable is calculated.

Step 4: Substitute the value of the calculated variable into one of the equations and calculate the value of the other variable.

Calculation:

Consider the problem,

Let x be the number of pairs of dirty socks and y be the number of dirty T-shirts.

There were three times as many pairs of dirty socks as T-shirts.

Thus,

x=3y

Rewrite x=3y in standard form,

x3y=0

Also, if Joe Slo’s roommate threw out x pairs of dirty socks and y dirty T-shirts, then total number of dirty clothes he threw was x+y. But the roommate tossed Joe’s dirty socks and T-shirts into the trash which was total of 44 items.

Thus,

x+y=44

Consider the equations,

x3y=0 …… (1)

x+y=44 …… (2)

Multiply equation (2) by 1,

1(x+y)=1(<

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