Question

the cost of 3 erasee, five sharpner and 7 pen is 105. the cost of 5 erasee, 8 sharpner and eleven pen is 166.what is the cost of one erasee, two sharpner and 3 pens​

Answer 1

ANSWER :

• ❖ If the cost of 3 erasers, 5 sharpeners and 7 pen is Rs. 105 and the cost of 5 erasers, 8 sharpeners and 11 pens is Rs. 166; then the cost of 1 erasee, 2 sharpeners and 3 pens will be Rs. 44.

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SOLUTION :

❒ Given :-

• Cost of 3 erasers , 5 sharpeners and 7 pens = Rs. 105

• Cost of 5 erasers, 8 sharpeners and 11 pens = Rs. 166

❒ To Find :-

• Cost of 1 eraser and 2 sharpeners and 3 pens = ?

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❒ Calculation :-

Let,

• Cost of 1 eraser be x

• Cost of 1 sharpener be y

• Cost of 1 pen be z

Then, we have to find,

• Cost of 1 eraser + 2 sharpeners + 3 pens = x + 2y + 3z = ?

According to first condition,

• 3x + 5y + 7z = 105 ———————> (1)

According to second condition,

• 5x + 8y + 11z = 166 ———————> (2)

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

• ✠ Eq. (1) × 2 ➨ (3x + 5y + 7z) × 2 = 105 × 2

➨ 6x + 10y + 14z = 210 −−−−−−−−−−>(3)

Now,

Subtracting Eq. (2) from Eq. (3), we get,

• ★ Eq. (3) − Eq. (2) ⇒ (6x + 10y + 14z) - (5x + 8y + 11z) = 210 - 166

⇒ 6x + 10y + 14z - 5x - 8y - 11z = 44

⇒ 6x - 5x + 10y - 8y + 14z - 11z = 44

⇒ x + 2y + 3z = 44

• As x + 2y + 3z = 44; hence, cost of 1 eraser, 2 sharpeners and 3 pens is Rs. 44.