Question

13. The cost of five pens, eight erasers and eleven
sharpeners is 354. The cost of three pens, five
erasers and seven sharpeners is 34. Find the cost
of one pen, one eraser and one sharpener (in ).

Answer 1

CORRECT QUESTION :

• ❖ The cost of five pens, eight erasers and eleven sharpeners is Rs. 354. The cost of three pens, five erasers and seven sharpeners is Rs. 34. Find the cost of one pen, one eraser and one sharpener.

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SOLUTION :

❒ Given :-

• Cost of 5 pens, 8 erasers and 11 sharpeners = Rs. 354

• Cost of 3 pens, 5 erasers and 7 sharpeners = Rs. 34

❒ To Find :-

• Cost of 1 pen, 1 eraser and 1 sharpener = ?

❒ Calculation :-

Let,

• Cost of 1 pen be x

• Cost of 1 eraser be y

• Cost of 1 sharpener be z

Then, we have to find :-

• x + y + z = ?

➮ According to first condition,

• 5x + 8y + 11z = 354 ———————> (1)

➮ According to second condition,

• 3x + 5y + 7z = 34 ———————> (2)

Now,

➮ Multiplying Eq. (1) with 2, we get :

$\bigstar \: \: \sf{ Eq. (1) \times 2 \implies \: 2 \times (5x + 8y + 11z) = 2 \times 354} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ \implies \: 10x + 16y + 22z = 708 \: \: - - - - - > (3)}$

And,

➮ Multiplying Eq. (2) with 3, we get :

$\bigstar \: \: \sf{ Eq. (2) \times 3 \implies \: 3 \times (3x + 5y + 7z) = 3 \times 34} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ \implies \: 9x + 15y + 21z = 102 \: \: - - - - - > (4)}$

➮ Subtracting Eq. (4) from Eq. (3), we get :

$\bigstar \: \: \sf{Eq. (3) - Eq. (4) \implies \: (10x + 16y + 22z)-(9x + 15y + 21z) = 708 - 102} \\ \\ \: \: \: \: \: \: \: \: \: \: \sf {\implies \: 10x + 16y + 22z-9x 15y - 21z = 606} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ \implies \: 10x - 9x + 16y - 15y + 22z - 21z = 606} \\ \\ \sf{\implies \: x + y + z = 606} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

• As x + y + z = 606; hence, cost of 1 pen, 1 eraser and 1 sharpener is Rs. 606.

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ANSWER :

• ❖ If the cost of five pens, eight erasers and eleven sharpeners is Rs. 354 and the cost of three pens, five erasers and seven sharpeners is Rs. 34; then the cost of one pen, one eraser and one sharpener is Rs. 606.