Q59. - Algebra 1

Question

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

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

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.

Step-by-Step Solution

Answer

Both the methods give the same value of $\mathbf{2940}$ calories burned.

Step 1. Given information.

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

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

Step 2. Write the Distributive property.

The distributive property of multiplication over addition or subtraction is given in below.

$a\left(b+c\right)=ab+ac$

Here $a, b$ and $c$ are real numbers.

Step 3. Write the expression.

Since the amount of Calories burnt by a person on any day is 420 $\times$ Time of surfing.

Therefore,

The number of calories burnt by a person on Monday $=420\times 1$

The number of calories burnt by a person on Tuesday $=420\times \frac{{\displaystyle 1}}{2}$

The number of calories burnt by a person on Wednesday $=420\times 0$

The number of calories burnt by a person on Thursday $=420\times 1$

The number of calories burnt by a person on Friday $=420\times 0$

The number of calories burnt by a person on Saturday $=420\times 2$

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

Step 4. Using the Distributive Property.

Total Calories burnt by a person in a week is given in below:

$\left(420\times 1\right)+\left(420\times \frac{1}{2}\right)+\left(420\times 0\right)+\left(420\times 1\right)+\left(420\times 0\right)+\left(420\times 2\right)+\left(420\times 2\frac{1}{2}\right)$

Apply the distributive property, the above expression can be written as in below:

$420\times \left(1+\frac{1}{2}+0+1+0+2+2\frac{1}{2}\right)$

Simplify the above expression.

$\begin{array}{l}420\times \left(4+\frac{1}{2}+\frac{5}{2}\right)=420\times \left(4+\frac{6}{2}\right)\\ =420\times \left(4+3\right)\\ =420\times 7\\ =2940\end{array}$

So, total Calories burnt by a person in a week $=2940$.

Step 5. Without Using the Distributive property.

Total Calories burnt by a person in a week are given below.

$\left(420\times 1\right)+\left(420\times \frac{1}{2}\right)+\left(420\times 0\right)+\left(420\times 1\right)+\left(420\times 0\right)+\left(420\times 2\right)+\left(420\times 2\frac{1}{2}\right)$

Simplify the above expression.

$420+210+0+420+0+840+1050$

So, total Calories burnt by a person in a week $=2940$.

Step 6. Conclusion.

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

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