Final answer:
By setting up a proportion (12/96 = x/240) and solving for x, we determine that the machine will produce 30 robots in 240 minutes, making answer (a) 30 robots the correct choice.
Step-by-step explanation:
To solve this problem, we need to set up a proportion because the number of robots produced is directly proportional to the amount of time the machine operates. The machine makes 12 robots in 96 minutes, so we can set the first part of our proportion as 12/96. Our goal is to find out how many robots the machine can make in 240 minutes.
Let's denote the number of robots produced in 240 minutes as x. Now our proportion looks like this: 12/96 = x/240.
To solve for x, we cross-multiply and get:
12 * 240 = 96 * x
Which simplifies to:
2880 = 96x
Now we divide both sides by 96 to solve for x:
2880 / 96 = x
x = 30.
Therefore, the machine will produce 30 robots in 240 minutes. The correct answer is (a) 30 robots.