Q64. - Algebra 1

Question

GARDENING On average, $7$ plants grow for every $10$ seeds of a certain type planted. Make a table to show the relation between seeds planted and plants growing for $50,100,150$ and $200$ seeds. Then state the domain and range and graph the relation.

Step-by-Step Solution

Answer

The domain of the relation is $\left\{50,100,150,200\right\}$ and the range of the relation is $\left\{35,70,105,140\right\}$.

The graph of the relation is:

Step 1. Given information.

We have on average $7$ plants grow for every $10$ seeds of a certain type planted.

 

To make a table to show the relation between seeds planted and plants growing for $50,100,150$ and $200$ seeds, state the domain and range and graph the relation.

Step 2. Apply concept.

First, calculate the unit rate, i.e., total plants growing for 1 seed and then multiply this unit rate for a given number of seeds. 

The domain is the set of all seeds available and range is the set of all plants growing.

Step 3. Calculation.

As plants growing for $10$ seeds $=7$

So, plants growing for $1$ seed $=\frac{7}{10}$

So, plants growing for $50$ seeds $=\frac{7\times 50}{10}=35$

Plants growing for $100$ seeds $=\frac{7\times 100}{10}=70$ 

Plants growing for $150$ seeds $=\frac{7\times 150}{10}=105$ 

Plants growing for $200$ seeds $=\frac{7\times 200}{10}=140$ 

The relation set is $\left\{\left(10,7\right),\left(50,35\right),\left(100,70\right).\left(150,105\right),\left(200,140\right)\right\}$ 

The graph of the above relation set is:

The domain of the relation is $\left\{50,100,150,200\right\}$ and the range of the relation is $\left\{35,70,105,140\right\}$.