5 pencil and 7 pens together coast rs 50 whereas 7 pencil and 5 pen together cost rs 46 find the cost of one pencil and that of one pen
Answers
Answer:
Cost of one pencil = Rs. 3 and that of one pen = Rs. 5
Step-by-step explanation:
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
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Answer :
- Cost of one pencil is Rs.3
- Cost of one pen is Rs.5
Given :
- 5 pencils and 7 pens together cost rupees 50
- 7 pencils and 5 pens together cost rupees 46
To find :
- Cost of one pencil and one pen
Solution :
- Let the cost of one pencil be x
- Let the cost of pen be y
According to question ,
》5x + 7y = 50
》7x + 5y = 46
5x + 7y = 50 is eq (1) and 7x + 5y = 46 is eq (2)
Now , we have to multiply 7 in equation (1) we get ,
》7 × 5x + 7y = 50
》35x + 49y = 350
35x + 49y = 350 is eq (3)
Now , we have to multiply 5 in equation (2) we get ,
》5 × 7x + 5y = 46
》35x + 25y = 230
35x + 25y = 230 is eq (4)
Now we have to equation 3 and equation 4 we get ,
》35x + 49y = 350 - 35x + 25y = 230
》24y = 120
》y = 120/24
》y = 5
Now Substituting the value of y = 5 in equation (2) we get,
》7x + 5y = 46
》7x + 5(5) = 46
》7x + 25 = 46
》7x = 21
》x = 21/7
》x = 3
- Cost of one pencil is Rs.3
- Cost of one pen is Rs.5