Chapter 12, Problem 13STP

a.

To determine

To find: An equation to represent the amount of hay needed to sustain $x$ horses for $d$ .

Answer to Problem 13STP

Amount of hay required $=10xd$ pounds.

Explanation of Solution

Given information:

A horse requires $10$ pounds of hay per day.

Given

A horse requires $10$ pounds of hay per day.

For each horse

  $1$ day $\to 10$ pounds of hay

Multiplying with $d$ on both sides

We get

  $\Rightarrow$ $1\times d$ days $\to 10\times d$ pounds of hay

  $\Rightarrow$ $d$ days $\to 10d$ pounds of hay

We got

For each horse for $d$ days it requires $10d$ pounds of hay

It means

For $d$ days

  $1$ horse $\to 10d$ pounds of hay

Multiplying with $x$ on both sides

We get

  $\Rightarrow$ $1\times x$ horses $\to 10d\times x$ pounds of hay

  $\Rightarrow$ $x$ horses $\to 10xd$ pounds of hay

Therefore,

For $x$ horses to sustain $d$ days they require $10xd$ pounds of Hay.

Amount of hay required $=10xd$ pounds.

b.

To determine

To find: Is your equation a direct, joint, or inverse variation.

Answer to Problem 13STP

It is a Joint Variation.

Explanation of Solution

Given information:

A horse requires $10$ pounds of hay per day.

We got

For $x$ horses to sustain $d$ days they require $10xd$ pounds of Hay.

Amount of hay required $=10xd$ pounds.

It is a Joint variation because here amount of hay required varies jointly with number of horses and number of days.

Therefore,

It is a Joint Variation.

c.

To determine

To find: How much hay do three horses need for the month of July

Answer to Problem 13STP

Amount of hay required $=930$ pounds

Explanation of Solution

Given information:

Number horses $=x=3$

Number of days $=d=31$ because it is given in month of July.

For $x$ horses to sustain $d$ days they require $10xd$ pounds of Hay.

Amount of hay required $=10xd$ pounds.

Number horses $=x=3$

Number of days $=d=31$ because it is given in month of July.

On substituting values

We get

Amount of hay required $=10xd$ pounds.

  $\Rightarrow$ Amount of hay required $=10\left(3\right)\left(31\right)$ pounds.

  $\Rightarrow$ Amount of hay required $=930$ pounds.

Therefore,

Amount of hay required $=930$ pounds