Question

The Table below shows the price, in dallarsfor the number of roses indicated.Inumbe or3.6a 다1215rosesPrice18at \36 43Dollars)• is the price proportional to the number of roses?know?• Find the cost of purching 30 roseshow do you

Answer 1

a) Since all the corresponding values of price and number of roses on the table follows the derived proportional equation the price is proportional to the number of roses.

b) The cost of purchasing 30 roses is $90

Step-by-step explanation:

From the given table we can observe that the price of roses increases as the number of roses increases.

this means the prices p is probably directly proportional to the number of roses n;

`\begin{gathered} p\propto n \\ p=kn \end{gathered}`

Let us find the constant of proportionality by substituting one of the corresponding values on the table;

At n=3, p= $9;

`\begin{gathered} p=kn \\ 9=k(3) \\ 3k=9 \\ (3k)/(3)=(9)/(3) \\ k=3 \end{gathered}`

So, the equation relating p to n is;

`p=3n`

Substituting other corresponding values into this equation, we can confirm that the equation is valid.

The cost of 30 roses can be calculated by substituting n=30 into the equation;

`\begin{gathered} p=3(30) \\ p=\text{ \$90} \end{gathered}`

Therefore, Since all the corresponding values of price and number of roses on the table follows the derived proportional equation the price is proportional to the number of roses.

The cost of purchasing 30 roses is $90