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The cost of a pen and a pencil used to be the same, but recently the cost of the pen was increased by ₹4, whereas, the cost of pencil became ₹6 less than 5 times its original value. After the revised cost, if the pen was more expensive than the pencil, what could have been the possible original value of both the products, if the initial price was a natural number?

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Answer:

The possible original values of both products are ₹2 or ₹1

Step-by-step explanation:

The question is a word problem leading to simultaneous equations

Let 'x' represent the initial value of the pen and pencil

Therefore;

The final cost of the pen = x + ₹4

The final cost of the pencil = 5·x - ₹6

x + ₹4 > 5·x - ₹6

∴  ₹4 + ₹6 > 5·x - x

₹10 > 4x

₹10/4 > x

₹2.5 > x

Given that x is a natural number, therefore

x ≤ ₹2

The possible original values of both products are ₹2 or ₹1

oladayoademosu

The possible original value of both products is ₹ 1 and  ₹ 2.

The question is a word problem

Let x represent the initial cost of the pen and pencil since they were initially the same price.

When the costs of the pen was increased by ₹4, its new price is x' = x + 4.

Also, the cost of pencil became ₹6 less than 5 times its original value. So, the new price of the pencil is x" = 5x - 6.

After the revised cost, if the pen was more expensive than the pencil, then we have x' > x".

So, x + 4 > 5x - 6

x - 5x > - 4 - 6

-4x > - 10

x < -10/-4

x < 2.5

Since the initial price of the both products was a natural number, the two natural number less than 2.5 are 1 and 2.

So, the possible original value of both products is ₹ 1 and  ₹ 2.

Learn more about word problems here:

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