the table below shows the number of different types of faucets sold over three months and the total selling…

the table below shows the number of different types of faucets sold over three months and the total selling price of the items. number of faucets sold and total selling price kitchen sink bathroom sink shower total selling price january 15 8 7 $2,830 february 17 12 8 $3,450 march 24 25 21 $6,680 the company makes a profit of 15% on every faucet sold. what is the profit on one shower faucet? $12.00 $13.50 $14.15 $18.00

the table below shows the number of different types of faucets sold over three months and the total selling price of the items. number of faucets sold and total selling price kitchen sink bathroom sink shower total selling price january 15 8 7 $2,830 february 17 12 8 $3,450 march 24 25 21 $6,680 the company makes a profit of 15% on every faucet sold. what is the profit on one shower faucet? $12.00 $13.50 $14.15 $18.00

Answer

Explanation:

Step1: Let the price of a kitchen - sink faucet be $x$, a bathroom - sink faucet be $y$, and a shower faucet be $z$.

Set up a system of equations based on the table: $$\begin{cases}15x + 8y+7z=2830\17x + 12y+8z=3450\24x + 25y+21z=6680\end{cases}$$

Step2: First, multiply the first equation by 3 and the second equation by 2 to eliminate $y$.

The first equation multiplied by 3: $45x + 24y+21z = 8490$. The second equation multiplied by 2: $34x + 24y+16z = 6900$. Subtract the second - new equation from the first - new equation: $(45x + 24y+21z)-(34x + 24y+16z)=8490 - 6900$ $45x+24y + 21z-34x - 24y-16z=1590$ $11x + 5z=1590$ (Equation 4).

Step3: Multiply the first equation by 25 and the third equation by 8 to eliminate $y$ again.

The first equation multiplied by 25: $375x+200y + 175z=70750$. The third equation multiplied by 8: $192x+200y+168z = 53440$. Subtract the third - new equation from the first - new equation: $(375x+200y + 175z)-(192x+200y+168z)=70750 - 53440$ $375x+200y + 175z-192x - 200y-168z=17310$ $183x+7z = 17310$ (Equation 5).

Step4: Multiply Equation 4 by 7 and Equation 5 by 5 to eliminate $z$.

Equation 4 multiplied by 7: $77x+35z = 11130$. Equation 5 multiplied by 5: $915x+35z = 86550$. Subtract the new Equation 4 from the new Equation 5: $(915x+35z)-(77x+35z)=86550 - 11130$ $915x+35z - 77x-35z=75420$ $838x=75420$ $x = 90$.

Step5: Substitute $x = 90$ into Equation 4.

$11\times90+5z=1590$ $990+5z=1590$ $5z=1590 - 990$ $5z=600$ $z = 120$.

Step6: Calculate the profit on one shower faucet.

The profit rate is 15%. The profit on one shower faucet is $0.15\times120=$18$.

Answer:

$18.00$