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Mathematics

Case Study II
There are two mobile-phone companies – P and Q, that offer different plans. Company P charges a monthly fee of ₹ 40 plus ₹ 0.5 per minute of talk time. Company Q charges a monthly service fee of ₹ 30 plus ₹ 1 per minute of talk time.

There are two mobile-phone companies – P and Q, that offer different plans. Company P charges a monthly fee of ₹ 40 plus ₹ 0.5 per minute of talk time. Company Q charges a monthly service fee of ₹ 30 plus ₹ 1 per minute of talk time. R.S. Aggarwal Mathematics Solutions ICSE Class 9.

Based on this information answer the following questions:

  1. The linear equation which expresses the plan of company P is :
    (a) y = 0.5x + 40
    (b) y = 40x + 0.5
    (c) y = x + 40.5
    (d) y = 40 − 0.5x

  2. The linear equation which expresses the plan of company Q is:
    (a) y = 30x + 1
    (b) y = x + 30
    (c) y = x − 30
    (d) y = 30x − 1

  3. How many minutes of talk time would yield equal expenditure from both companies?
    (a) 10 minutes
    (b) 15 minutes
    (c) 20 minutes
    (d) 25 minutes

  4. Manisha took the plan of company P and used 400 minutes of talk time. She spent:
    (a) ₹240
    (b) ₹430
    (c) ₹220
    (d) ₹215

  5. If in a month, Anurag wants to use only 300 minutes of talk time, then which company’s plan is better for him?
    (a) Company P
    (b) Company Q
    (c) Both offer the same plan
    (d) Can’t be determined

Linear Equations

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Answer

1. Given,

Let x = number of minutes, and y = total cost in ₹

Company P charges: ₹40/month + ₹0.5/min talk time

⇒ y = 0.5x + 40.

Hence, Option (a) is the correct option.

2. Given,

Company Q charges: ₹30/month + ₹1/min talk time

⇒ y = x + 30

Hence, Option (b) is the correct option.

3. If the expenditure is equal, then equating the values of y from part (1) and (2)

⇒ 0.5x + 40 = x + 30

⇒ 40 - 30 = x - 0.5x

⇒ 10 = 0.5x

⇒ x = 100.5\dfrac{10}{0.5} = 20 minutes.

Hence, Option (c) is the correct option.

4. Given,

Manisha used 400 minutes on Company P. Calculating, the money spent by her,

⇒ y = 0.5x + 40

⇒ y = 0.5(400) + 40

⇒ y = 200 + 40

⇒ y = ₹ 240.

Hence, option (a) is the correct option.

5. Given,

Anurag uses 300 minutes,

Cost if he took Company P's plan.

⇒ y = 0.5x + 40

⇒ y = 0.5(300) + 40

⇒ y = 150 + 40

⇒ y = ₹ 190

Cost if he took Company Q's plan.

⇒ y = 1x + 30

⇒ y = 300 + 30

⇒ y = ₹ 330.

Thus, Anurag gets benefit if he uses company P's plan.

Hence, option (a) is the correct option.

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