Question

form q pair of linear equation in two variable for the following information. "there some 50 paisa and 25 paisa coins in a bag. the total number of coins are 140 and the valve of all coins is 50 rs.​

Answer 1

Answer:

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Answer 2

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Hint:Here, we have two unknowns, i.e., number of 2525 paisa coins and number of 5050 paisa coins. We will assume these as unknown variables. We have been given the total value of coins and the total number of coins. We will thus use these two given values to make a pair of linear equations in two variables.

Complete step-by-step answer:

Let the Number of 2525 paisa coins =x=x

Let the Number of 5050 paisa coins =y=y

Now, we have two unknowns. So, we will have to have two equations that will describe the relationships between the unknowns and, if asked, we can find the number of 2525 paisa and 5050 paisa coins after solving these two equations.

Let’s think about the information that are given to us in the problem. We are given the total number of coins in the bag. Also, we have been given the total value of coins. Each of these pieces of information will produce an equation.

“The total number of coins are 140140”:

⇒x+y=140⇒x+y=140 ………………………………… Eqn I

“the value of coins is rupees 5050”:

⇒⇒ Total value of 2525 paisa coins ++ Total value of 5050 paisa coins =5000=5000

(∵50∵50rupees =5000=5000paisa)

Mathematically,

⇒25x+50y=5000⇒25x+50y=5000 ⇒25(x+2y)=5000⇒25(x+2y)=5000

⇒x+2y=200⇒x+2y=200 ………………………………… Eqn II

Hence, the pair of linear equations in two variables for the given information is:

x+y=140x+y=140

x+2y=200x+2y=200

Note:If we are asked to get the number of coins of both types, we can also use a direct formula as well. We can use a trick if this Two-Coin problem would have been asked in a competitive exam.

Alternative method:

Let total value of coins (in rupees) =V=V

Let total number of coins =N=N

Let value of coin_1 (in rupees) =a=a

Let value of coin_2 (in rupees) =b=b

Let the number of coin_1 =x=x

Let the number of coin_1 =y=y

Then,

Number of coin_1 =x=x=bN−Vb−a=bN−Vb−a…………. Eqn I

Number of coin_2 =y=y=N−x=N−x…………. Eqn II

In this problem,

V=50V=50

N=140N=140

Let xx be the number of 5050 paisa (i.e., 0.500.50 rupee) coins. Thus, a=0.50a=0.50.

Let yy be the number of 2525 paisa (i.e., 0.250.25 rupee) coins. Thus, b=0.25b=0.25.

As per equation I,

Number of 5050 paisa coins =x=x=bN−Vb−a=bN−Vb−a

⇒x=0.25×140−500.25−0.50=35−50−0.25=−15−0.25=150025⇒x=0.25×140−500.25−0.50=35−50−0.25=−15−0.25=150025=60=60

⇒x=60⇒x=60

As per equation II,

Number of 2525 paisa coins =y=y=N−x=N−x

⇒y=140−60=80⇒y=140−60=80

⇒y=80⇒y=80

∴∴ Number of 2525 paisa coins =80=80

∴∴ Number of 5050 paisa coins =60=60

Cross-check

Total Value (in Rupees) == no. of 2525 paisa coins ×× 0.250.25 ++ no. of 5050 paisa coins ×× 0.500.50

=80×0.25+60×0.50=80×0.25+60×0.50

=20+30=20+30

=50=50

Thus, our answer is correct. (Hence proved)