Chapter 4.1, Problem 41PPS

To determine

Two equivalent expression and total cost.

Answer to Problem 41PPS

  $2\left(7\right)+2\left(8\right)$ and $2\left(7+8\right)$

  $\$30$

Explanation of Solution

Given information:

Cost for adults $=\$8$

Cost for students $=\$7$

Number of adults $=2$

Number of students $=2$

Concept Used:

Distributive Property: The product sum or difference of two or more numbers inside a parentheses with another number outside the parentheses is equivalent to the sum or difference of product of number outside the parentheses with each number inside the parenthesis. i.e.-

  $a\left(b+c-d\right)=ab+ac-ad$

Calculation:

The expression for total cost will be the sum of cost for admission of two students andcost for admission of two adults, i.e.

  $2\left(7\right)+2\left(8\right)$

This expression can also be written as

  $2\left(7\right)+2\left(8\right)=2\left(7+8\right)\left(\text{Distributive property}\right)$

This can further be evaluated as-

  $\begin{array}{l}2\left(7\right)+2\left(8\right)=2\left(7+8\right)\\ \Rightarrow 2\left(7\right)+2\left(8\right)=2\left(15\right)\\ \Rightarrow 2\left(7\right)+2\left(8\right)=\$30\end{array}$

Total wage for babysitting is $\$30$