Chapter 1.4, Problem 59HP

To determine

To explain the distributive property can be used to calculate quickly and compare methods of finding the total Calories burned with and without using the distributive property.

Explanation of Solution

Given:

A a person burns 420 Calories per hour by surfing. The time he spent surfing in one week is as shown:

Day	Mon	Tue	Wed	Thu	Fri	Sat	Sun
Time(h)	1	$\frac{1}{2}$	0	1	0	2	$2\frac{1}{2}$

Concept used:

The Distributive Property: $ab+ac=a(b+c)$

Calculation:

The amount of Calories burnt by a person on any day $=420\times$ Time of surfing

The amount of Calories burnt by a person on Monday $=420\times 1$

The amount of Calories burnt by a person on Tuesday $=420\times \frac{1}{2}$

The amount of Calories burnt by a person on Wednesday $=420\times 0$

The amount of Calories burnt by a person on Thursday $=420\times 1$

The amount of Calories burnt by a person on Friday $=420\times 0$

The amount of Calories burnt by a person on Saturday $=420\times 2$

The amount of Calories burnt by a person on Sunday $=420\times 2\frac{1}{2}$

Method 1: Without using distributive property

Total Calories burnt by a person in a week $=(420\times 1)+(420\times \frac{1}{2})+(420\times 0)+(420\times 1)+(420\times 0)+(420\times 2)+(420\times 2\frac{1}{2})$

Total Calories burnt by a person in a week $=420+210+0+420+0+840+1050$

Total Calories burnt by a person in a week $=2940.$

Method 2: Using distributive property

Total Calories burnt by a person in a week $=(420\times 1)+(420\times \frac{1}{2})+(420\times 0)+(420\times 1)+(420\times 0)+(420\times 2)+(420\times 2\frac{1}{2})$

Total Calories burnt by A person in a week $=420\times (1+\frac{1}{2}+0+1+0+2+2\frac{1}{2})$ [Q$ab+ac=a(b+c)]$

Total Calories burnt by a person in a week $=420\times 7$

Total Calories burnt by a person in a week $=2940$

The solution remains same irrespective of the distribution property is used or not.

The use of this property reduces the time of calculations.

Conclusion:

From the above two methods, method using distributive property helps to solve the problem quicker.

The amount of calories burned is same irrespective of the method used.