Question

A company, which is making 200 mobile phones each week, plans to increase its production. The number of mobile phones produced is to be increased by 20 each week from 200 in week 1 to 220 in week 2, to 240 in week 3 and so on. (a) Find the number of weeks for production reach 600 unit mobile phone. The company then plans to continue to make 600 mobile phones each week.

Answer 1

Explanation:To find the number of weeks it will take for the production to reach 600 mobile phones per week, you can set up an equation based on the increasing production rate.

Let's denote:

- W as the number of weeks.

- P as the number of mobile phones produced per week.

In the first week, 200 mobile phones are produced. In the second week, it increases by 20, so it's 220. In the third week, it increases by 20 again, making it 240, and so on. This is an arithmetic progression where the first term (a) is 200, the common difference (d) is 20, and we want to find the number of weeks (W) when P = 600.

The formula for an arithmetic progression is given by:

P = a + (W - 1) * d

Substitute the values:

600 = 200 + (W - 1) * 20

Now, solve for W:

400 = (W - 1) * 20

Divide both sides by 20:

W - 1 = 20

Now, add 1 to both sides:

W = 20 + 1

W = 21

So, it will take 21 weeks for the production to reach 600 mobile phones per week.

After that, if the company plans to continue making 600 mobile phones each week, there's no change in the production rate, and they will consistently produce 600 mobile phones per week from week 21 onward.