Chapter 6.7, Problem 14E

To determine

To calculate: The number of African seeds that will sprout on planting

  $20$ more seeds.

Answer to Problem 14E

Number of seeds that will sprout if $20$ more seeds are planted = $15$

Explanation of Solution

Given information:

Number of African seeds planted = $30$

Number of African seeds that sprouted = $9$

  $20$ more seeds will be planted.

Calculation:

To find the number of African seeds that will sprout, find experimental probability that a seed will sprout.

  $\begin{array}{l}\\ P(\text{a seed will sprout)}=\frac{9}{30}\\ \text{ =}\frac{3}{10}\text{ [Express in simplest form]}\end{array}$

Number of seeds that will be planted = $30+20=50$

Let $x$ be the number of seeds that will sprout if $20$ more seeds are planted. Write and solve a proportion.

  $\begin{array}{l}\frac{x}{50}=\frac{3}{10}\text{ [Write proportion]}\\ x\cdot 10=3\cdot 50\text{ [Form cross product]}\\ x.10=150\text{ [Multiply]}\\ x=15\text{ [Divide both sides by 10]}\end{array}$

Therefore, the number of seeds that will sprout if $20$ more seeds are planted is $15$