Question

Rohan went to the stationary shop to purchase pens, erasers, and rulers. He purchased more number of pens than erasers and more number of erasers than rulers. He purchased at least 10 items of each type. Total number of items purchased is 35.

If each pen cost is rs 20,each ruler cost rs 2 , and each eraser cost rs 5, find the minimum amount in rs that Rohan spent for purchasing items​

Answer 1

Given:

Number of pens > Number of Eraser > Number of Rulers

He purchased at least 10 items of each time.

He needs to purchase 35 items.

To FInd:

The minimum amount that he needs to spend.

Solution

Define x, y and z

Let the total number of pens purchased = 10 + x

Let the total number of eraser purchased = 10 + y

Let the total number of rulers purchased = 10 + z

The total number of items purchased is 35:

(10 + x) + (10 + y) + (10 + x) = 35

x + y + z = 5

Solve x, y and z:

Pen = Rs 20,

Eraser = Rs 5

Ruler = Rs 2

we know that:

⇒ x + y + z = 5

⇒ x > y > z:

if we add 1 to z, we need to add 2 to y and 3 to x

⇒ 1 + 2 + 3 = 6

⇒ 30 + 6 = 36

⇒ There will be one too many

If we do not add to z, we add 2 to y and 3 to x

⇒ 2 + 3 = 5

⇒ 30 + 5 = 35

⇒ we achieve the target of 35 items

Find the cost of items:

Rulers = 10

Rulers =  Rs 2 x 10

Rulers = Rs 20

Erasers = 10 + 2

Erasers = 12

Erasers = R5 x 12

Erasers = Rs 60

Pens = 10 + 3

Pens = 13

Pens = Rs 20 x 13

Pens = Rs 260

Total = 20 + 60 + 260

Total = Rs 340

Answer: The total cost is Rs 340 for 10 Rulers, 12 Erasers and 13 Pens