Question

5 pencils and 7 pens together cost 50 rs, whereas 7 pencils and 5 pens together
cost 46 rs. Find the cost of one pencil and that of one pen.​

Answer 1

Answer:

Let cost of pencil be Rs. x

Cost of pens be Rs. y

5 pencils and 7 pens together cost Rs. 50,

So we get

5x+7y=50

Subtract 7y both side we get

5x=50–7y

Divide by 5 we get

x=10−

5

7

y

Plug value of y which is factor of 5 to get whole number so plug y=5,10,15 we get

fory=5

x=10−

5

7

y=10−7=3

for y=10

x=10−

5

7

y=10−14=−4

fory=15

x=10−

5

7

y=10−21=−11

Therefore, the required points are (3,5),(−4,10),(−11,15).

Given that 7 pencils and 5 pens together cost Rs. 46

7x+5y=46

Subtract 7x both side we get

5y=46–7x

Divide by 5 we get

y=9.2–1.4x

Plug x=0,2,4 we get

for x=0

y=9.2–0=9.2

for x=2

y=9.2–2.8=6.4

forx=4

y=9.2–5.6=3.6

Therefore, the required points are (0,9.2),(2,6.4),(4,3.6).

The graph is as shown below:

Since the point of intersection is (3,5),

Hence, the cost of one pencil is Rs. 3 and the cost of one pen is Rs. 5