Combined, two production lines can make 315 light bulbs in 1 hour. Production line A produces light bulbs 1.1 times faster than production line B. Using a rational equation, which of the following correctly calculates how many light bulbs can be produced in 1 hour using only production line A?(1 point)

Question

Responses

300 light bulbs
300 light bulbs

165 light bulbs
165 light bulbs

150 light bulbs
150 light bulbs

158 light bulbs

Answer 1

Let the rate of production for line B be \( x \) light bulbs per hour. Therefore, the rate of production for line A is \( 1.1x \) light bulbs per hour.

Combined, the two production lines can produce:

\[ x + 1.1x = 2.1x \]

According to the problem, together they can produce 315 light bulbs in 1 hour. Thus, we can set up the equation:

\[ 2.1x = 315 \]

Now, solving for \( x \):

\[ x = \frac{315}{2.1} = 150 \]

Now that we know the rate of production for line B is 150 light bulbs per hour, we can find the rate for production line A:

\[ 1.1x = 1.1 \times 150 = 165 \]

Thus, production line A can produce 165 light bulbs in 1 hour.

The correct response is 165 light bulbs.