if the cost of 37 pen and 53 pencil is 320 and 37 pencil and 53 pen cost 400 find cost of 2 pen
Answers
Answer:
Step-by-step explanation:
Let the cost of a pen and cost of a pencil be Rs x and Rs y respectively. It is given that 37 Pens and 53 pencils together cost Rs. 320. So, 37x + 53y = 320 (1)
It is also given that 53 Pens and 37 Pencils together cost Rs. 400. So, 53x + 37y = 400 (2)
Equations (1) and (2) can be solved in any of the method such as: elimination method, substitution method or cross multiplication method. There is another way of solving equations of the form ax + by = c and bx + ay = d.
Add and subtract these two equations and reduce these equations to the standard form.
Let these equations be (3) and (4). Now, equations (3) and (4) can be easily solved to obtain x and y.
Adding and subtracting equations (1) and (2); 37x + 53y + 53x + 37y = 320 + 400 and 37x + 53y - 53x - 37y = 320 - 400 OR, 90x + 90y = 720 and -16x + 16y = -80 OR, 90(x + y) = 720 and -16(x - y) = -80 OR, x + y = 8 (3) And x - y = 5 (4)
Adding (3) and (4); 2x = 13 OR, x = 6.5
Substituting the value of x in equation (3); y = 1.5
Therefore, the cost of a pen and a pencil are Rs 6.5 and Rs 1.5 respectively.
hope this helps you
Answer:
13
Step-by-step explanation:
37 pen and 53 pencil is 320
37 pens + 53 pencils = 320 ------- [ 1 ]
37 pencil and 53 pen cost 400
53 pens + 37 pencils = 400 ------- [ 2 ]
[ 1 ] x 53:
1961 pens + 2809 pencils = 16960 ------- [ 1a ]
[2] x 37:
1961 pens + 1369 pencils = 14800 ------- [ 2a ]
[1a ] - [2a] :
1440 pencils = 2160
1 pencil = 1.5
Sub 1 pencil = 1.5 into equation [ 1]:
37 pens + 53(1.5) = 320
37 pens + 79.5 = 320
37 pens = 240.5
1 pen = 6.5
Find 2 pens:
1 pen = 6.5
2 pens = 6.5 x 2 = 13
Answer: 2 pens cost 13.