3 bags and 4 pens together cost ₹ 257 whereas 4 bags and 3 pens together cost ₹324. Find the total cost of 1 bag and 10 pens.

Given:

3 bags and 4 pens together cost ₹ 257 whereas 4 bags and 3 pens together cost ₹324.

To do:

We have to find the total cost of 1 bag and 10 pens.

Let the cost of one bag and one pen be $x$ and $y$ respectively.

According to the question,

$3x + 4y = 257$.....(i)

$4x + 3y = 324$.....(ii)

Multiplying equation (i) by 3 on both sides, we get,

$3(3x+4y)=3(257)$

$9x+12y=771$.....(iii)

Multiplying equation (ii) by 4 on both sides, we get,

$4(4x+3y)=4(324)$

$16x+12y=1296$.....(iv)

Subtracting equation (iii) from equation (iv), we get,

$(16x+12y)-(9x+12y)=1296-771$

$16x-9x+12y-12y=525$

$7x=525$

$x=\frac{525}{7}$

$x=75$

Substituting $x=75$ in equation (ii), we get,

$4(75)+3y=324$

$300+3y=324$

$3y=324-300$

$3y=24$

$y=\frac{24}{3}$

$y=8$

$\Rightarrow 10y=10(8)=80$

$x=75$ and $10y=80$

$x+10y=75+80=155$

The total cost of 1 bag and 10 pens is Rs. 155. 

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Updated on: 10-Oct-2022

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