Question

if 8 pens and 7 pencils cost $3.37 while 5 pens and 11 pencils cost $3.10, how much does each pen and pencil cost?

Answer 1

Let a=number of pens and b=number of pencils.
8a+7b=3.37; 5a+11b=3.10.
To eliminate a variable multiply the first eqn by 5 and the second by 8:
40a+35b=16.85, 40a+88b=24.80.
Subtract these equations: 53b=7.95, b=$0.15. So 5a=3.10-1.65=$1.45, a=$0.29.
Pens are $0.29 each and pencils $0.15.

Answer 2

Answer with Step-by-step explanation:

Let x be the cost of 1 pen and y be the cost of 1 pencil

8 pens and 7 pencils cost $3.37 while 5 pens and 11 pencils cost $3.10

8x+7y= 3.37  -----------------(1)

and 5x+11y= 3.10  -----------------(2)

equation (1)×5-equation(2)×8

5(8x+7y)-8(5x+11y)=3.37×5-3.10×8

40x+35y-40x-88y= -7.95

-53y = -7.95

y= 0.15

Putting y=0.15 in equation (1), we get

8x+7×0.15=3.37

8x+1.05=3.37

8x=2.32

x=0.29

Hence, Cost of 1 pen=$ 0.29

Cost of 1 pencil= $ 0.15