EBK PRE-ALGEBRA
EBK PRE-ALGEBRA
12th Edition
ISBN: 9780358403685
Author: Larson
Publisher: HM CC
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Chapter 7.1, Problem 59E

a.

To determine

Sum of 40% of x and 60% of y is equal to 100% of the sum x+y or not.

a.

Expert Solution
Check Mark

Answer to Problem 59E

The sum of 40% of x and 60% of y is not equal to 100% of the sum x+y .

Explanation of Solution

Given:

   x and y represent two different whole numbers.

  40% of x is added to 60% of y

  100% of the sum x+y .

Calculation:

As per the given problem

Calculate 40% of x

  40% of x=40100⋅x     [write percent as fraction]               =0.4x          [simplify and convert fraction to decimal]

Then calculate 60% of y

  60% of y=60100⋅y     [write percent as fraction]               =0.6y          [simplify and convert fraction to decimal]

Now, add

  40% of x to 60% of y

  40% of x+60% of y=0.4x+0.6y   

Calculate 100% of the sum x+y

  100% of (x+y)=100100(x+y)   [write percent as fraction]                          =(x+y)          

As,

   0.4x+0.6y≠(x+y)

Therefore,

  40% of x+60% of y≠100% of (x+y)

Conclusion:

The sum of 40% of x and 60% of y is not equal to 100% of the sum x+y .

b.

To determine

The average of the 40% of x and 60% of y is equal to 50% of the sum x+y or not.

b.

Expert Solution
Check Mark

Answer to Problem 59E

The average of the 40% of x and 60% of y is not equal to 50% of the sum x+y .

Explanation of Solution

Given:

   x and y represent two different whole numbers.

  40% of x=0.4x

  60% of y=0.6y

Calculation:

As per the given problem

  40% of x=0.4x

  60% of y=0.6y

Average of 40% of x and 60% of y = (0.4x+0.6y)2

Calculate 50% of the sum x+y .

  50% of (x+y)=50100⋅(x+y)        [write percent as fraction] ⇒(x+y)2               [simplify]

As,

  (0.4x+0.6y)2≠(x+y)2 

Therefore,

Average of 40% of x and 60% of y

  ≠50% of (x+y)

Conclusion:

The average of the 40% of x and 60% of y is not equal to 50% of the sum x+y .

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Chapter 7.1, Problem 58E
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Chapter 7.1, Problem 60E

Chapter 7 Solutions

EBK PRE-ALGEBRA

Ch. 7.1 - Prob. 1CCh. 7.1 - Prob. 2CCh. 7.1 - Prob. 3CCh. 7.1 - Prob. 4CCh. 7.1 - Prob. 5CCh. 7.1 - Prob. 6CCh. 7.1 - Prob. 7CCh. 7.1 - Prob. 8CCh. 7.1 - Prob. 9CCh. 7.1 - Prob. 1E
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