If 11 pens and 19 pencils together cost ₹ 502, while 19 pens and 11 pencils together cost ₹ 758, how much do 3 pens and 6 pencils cost together?
Linear Equations
4 Likes

Question

If 11 pens and 19 pencils together cost ₹ 502, while 19 pens and 11 pencils together cost ₹ 758, how much do 3 pens and 6 pencils cost together?

KnowledgeBoat · Accepted Answer

Let the cost of a pen be ₹ x and ₹ y be the cost of a pencil. Given, 11 pens and 19 pencils together cost ₹ 502. ⇒ 11x + 19y = 502 ........(1) Given, 19 pens and 11 pencils together cost ₹ 758. ⇒ 19x + 11y = 758 .........(2) Subtracting equation (1) from equation (2), we get : ⇒ 19x + 11y - (11x + 19y) = 758 - 502 ⇒ 19x - 11x + 11y - 19y = 256 ⇒ 8x - 8y = 256 ⇒ 8(x - y) = 256 ⇒ x - y = ⇒ x - y = 32 ⇒ x = 32 + y .....(3) Substituting value of x in equation (1), we get : ⇒ 11x + 19y = 502 ⇒ 11(32 + y) + 19y = 502 ⇒ 352 + 11y + 19y = 502 ⇒ 30y = 502 - 352 ⇒ 30y = 150 ⇒ y = ⇒ y = ₹ 5. Substituting value of y in equation (3), we get : ⇒ x = 32 + y ⇒ x = 32 + 5 ⇒ x = ₹ 37. The amount to buy the 3 pens and 6 pencils is, ⇒ 3x + 6y ⇒ 3 × 37 + 6 × 5 ⇒ 111 + 30 ⇒ ₹ 141. Hence, 3 pens and 6 pencils costs ₹ 141.

Mathematics

If 11 pens and 19 pencils together cost ₹ 502, while 19 pens and 11 pencils together cost ₹ 758, how much do 3 pens and 6 pencils cost together?

Linear Equations

Related Questions

A number of two digits exceeds four times the sum of its digits by 6, and the number is increased by 9 on reversing its digits. Find the number.

The sum of the digits of a two-digit number is 12. If the digits are reversed, the new number is 12 less than twice the original number. Find the original number.

5 kg sugar and 7 kg rice together cost ₹ 258, while 7 kg sugar and 5 kg rice together cost ₹ 246. Find the total cost of 8 kg sugar and 10 kg rice.

One year ago a man was four times as old as his son. After 6 years, his age exceeds twice his son’s age by 9 years. Find their present ages.