Jack's tile worker charges $$ 7$ per room, and they receive a $$ 5$ service charge for the entire day. Luke's tile worker charges $$ 3$ per room and they receive a $$ 21$ service charge for the entire day. Find the number of rooms for which the total cost of both tile workers is the same.

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Solution

The correct option is C 4
Let $x$ be the number of rooms.

The cost of Jack' tiles work per room $= 7$
The cost of Jack's tiles work for $x$ number of rooms $= 7 \times x = 7 x$
And they receive a service charge $= 5$
Total cost of Jack's tiles work $= 7 x + 5$

The cost of Luke's tiles work per room $= 3$
The cost of Luke's tiles work for $x$ number of rooms $= 3 \times x = 3 x$
And they receive a service charge $= 21$
Total cost of Luke' tiles work $= 3 x + 21$

Given, the total cost of both tiles work are equal.
$\Rightarrow 7 x + 5 = 3 x + 21$

Step 1: Subtract both sides of the equation by 5
$\Rightarrow 7 x + 5 - 5 = 3 x + 21 - 5 \Rightarrow 7 x = 3 x + 16$

Step 2: Subtract both sides of the equation by $3 x$
$\Rightarrow 7 x - 3 x = 3 x + 16 - 3 x$
$\Rightarrow 4 x = 16$

Step 3: Now, divide both sides by 4
$\Rightarrow \frac{4 x}{4} = \frac{16}{4} \Rightarrow x = 4$

Hence, the required number of rooms is $4.$

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Jack's tile worker charges $7 per room, and they receive a $5 service charge for the entire day. Luke's tile worker charges $3 per room and they receive a $21 service charge for the entire day. Find the number of rooms for which the total cost of both tile workers is the same.

Jack's tile worker charges $$ 7$ per room, and they receive a $$ 5$ service charge for the entire day. Luke's tile worker charges $$ 3$ per room and they receive a $$ 21$ service charge for the entire day. Find the number of rooms for which the total cost of both tile workers is the same.