Chapter 6.4, Problem 22PPE

To determine

To calculate: Amount of each perfume to make a perfume that can be sold for $\$63$ .

Answer to Problem 22PPE

perfume $A$ is used $2.1$ oz and $B$ is used $0.9$ oz

Explanation of Solution

Given information: A perfume maker has stocks of two perfumes on hand. Perfume $A$ sells for $\$15$ per ounce. Perfume $B$ sells for $\$35$ per ounce.

Calculation:

Let’s assume $x$ ounces of $A$ and $y$ ounces of $B$ is taken to make the final perfume.

Now, total ounces in final perfume bottle is $3oz$ , $\therefore x+y=3$.......(i)

The cost of $A$ in final perfume is, $15x$

The cost of $B$ in final perfume is, $35y$

Now, the total cost is, $15x+35y=63$......(ii)

Now, multiply equation (i) with 15 and subtract it from (ii),

  $\therefore 15x+35y-15(x+y)=63-45$

  $\therefore y=0.9$ oz

Substitute value of $y$ into equation (i), $\therefore x=3-0.9=2.1$ oz

Therefore, perfume $A$ is used $2.1$ oz and $B$ is used $0.9$ oz