Question

5 pencils and 7 pens together cost rupees 50 where as 7 pencils and 5 pens cost rupees 46. find the cost of 2 pencils and 3 pens
options
a) 42
b) 39
c) 21
d) 16​

Answer 1

Answer:

Rupees 21

Step-by-step explanation:

*Given:-

• cost of 5 pencils and 7 pens=50

• cost of 7 pencils and 5 pens=46

*Find:-

• Cost of 2 pencils and 3 pens=?

*Solution:-

------>Consider the number of pencils =x

------>Consider the number of pens=y

So, for the equation 1:-

------> the number of pencils =5x

------->the number of pens=7y

For the equation 2:-

------->the number of pencils=7x

-------->the number of pens=5y

Now we have to form the equations:-

5x+7y=50 (equation 1)

7x+5y=46 (equation 2)

We know the rules that the :-

(1) Coefficient of the variable of the first equation should be equal to the coefficient of the variable of second equation.

(2) If the coefficient of the variables are equal but have same signs i.e (-) or (+), we have to subtract the equations from each other.

(3) If the coefficient of the variables are equal but have different signs i.e (-) or (+), we have to add the equations with each other.

According to the rules, first we have to make the coefficient of the variable same.

Here, I'm gonna choose variable x, you can choose variable y as well.

5x+7y=50 (equation 1)×7

7x+5y=46 (equation 2)×5

35x+49y=350(equation 1)

35x+25y=230(equation 2)

------>Same signs , so we have to subtract the equations:-

35x+49y=350

-35x-25y=-230

_________________

0 + 24y = 120

_________________

---->24y=120

---->y=120/24

---->y=5

Substitute the value of ybin any one of the equation:-

• 5x+7y=50

• 5x+7(5)=50

• 5x+35=50

• 5x=50-35

• 5x=15

• x=3

Verification:-

1. 5x+7y=50

5(3)+7(5)=50

15+35=50

50=50

2. 7x+5y=46

7(3)+5(5)=46

21+25=46

46=46

Cost of 2 pencils and 3 pens:-

---->2x=pencils

---->2(3)=6

---->3y=pens

---->3(5)=15

---->6+15=21

The cost of 2 pencils and 3 pens is rupees 21.

Hence verified.