Chapter 7, Problem 7CR

To determine

The total cost of the food and justify your answer by using Distributive Property

Answer to Problem 7CR

The total cost from mental math is $\$30$

The total cost using Distributive Property is $\$30$

Explanation of Solution

Given information:

The Stuart family has 5 members and they each purchase a soda at $2.50 each and a hotdog at $3.50 each

Concept used:

• The distributive property of binomials (FOIL):

    $\left(a+b\right)\left(c+d\right)=a\cdot c+a\cdot d+b\cdot c+b\cdot d$

• Left Distributive property: $a\left(b+c\right)=a\cdot b+a\cdot c$
• Exponent property: $x^n\cdot x^m=x^{n+m}$

Calculation:

In order to find the total cost of the food by mental math, observe that each person purchase a soda at $2.50 and a hotdog at $3.50. So each person purchased for $2.50+3.50=6$ dollars. Now since there are total 5 members and each purchased for $6, so the total cost of food would be 5 times the cost of the food of one, that is, $5\times 6=\$30$ .

Now, to verify it using distributive property, simplify as shown below

  $\begin{array}{c}\text{Total}\text{members}=5\\ \text{Soda}\text{purchase}=2.50\\ \text{Hotdog}\text{purchase}=3.50\\ \text{Total}\text{cost}=5\left(2.50+3.50\right)\\ =5\left(6\right)\\ =30\end{array}$

Thus, the total cost using Distributive Property is $\$30$