Chapter 8.4, Problem 14GP

To determine

How many roses are in each arrangement.

Answer to Problem 14GP

  $12\text{roses}$

Explanation of Solution

Given:

Vaneesha makes 7 identical flower arrangements for the tables at a banquet.

Each arrangement contain some roses and 9 tulips, total 147 flowers she uses.

Concept Used:

Distributive property:

Left Distributive property: $a\left(b\pm c\right)=a\cdot b\pm a\cdot c$

Right Distributive property: $\left(a\pm b\right)c=a\cdot c\pm b\cdot c$

• To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
• To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
• To get rid of a number in division from one side, multiply the same number both sides of equal sign.

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to find how many roses are in each arrangement, let number of roses be r and 9 tulips as given, now adding both the roses and tulips and then multiplying it by 7 because total 7 identical flower arrangements, then the equation is equal to 147 the total flowers to make the arrangement, now the equation is as shown below:

  $7\left(r+9\right)=147$

Now, to solving the equation first using distributive property on left side of the equation and then isolate the variable term r on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate r on left side, first subtract 63 from both sides and then divide both sides by 7 and then simplify further as shown below,

  $\begin{array}{l}7\left(r+9\right)=147\\ 7\cdot r+7\cdot 9=147\\ 7r+63=147\\ 7r+63-63=147-63\\ 7r=84\\ \frac{7r}{7}=\frac{84}{7}\\ r=12\end{array}$

So, there are 12 roses in each arrangement.