Mathematics

# a) six pens and five pencils cost $2.50 while three pens and two pencils cost$1.15 . what will be the cost of a pen and 4 pencils . please help me

#### rishimisra15

4 years ago

Let pen's cost be x and pencil's cost be y.

6x + 5y = 2.50
3x + 2y = 1.15

Thus, 3x = 1.15 - 2y
Therefore, 6x = 2.30 - 4y

Substituting the value of 6x ;

(2.30 - 4y) + 5y = 2.50

or, 2.30 + y = 2.50

=> y = 0.20.

Substituting the value of y ;

6x = 2.30 - 4(0.20)
6x = 2.30 - 0.80 = 1.5
6x = 1.5
=> x = 0.25

Thus, 1 pen costs 0.25 $and 1 pencil costs 0.20$.

Thus, cost of one pen is 0.25$. Cost of 4 pencils is 0.80$

0.25$+ 0.80$ = 1.05\$

#### yassautumn

4 years ago

x - pen
y - pencil

$6x+5y=2.5\\ 3x+2y=1.15\\\\ 6x+5y=2.5\\ -6x-4y=-2.3\\ --------\\ y=\0.2\\\\ 6x+5\cdot0.2=2.5\\ 6x+1=2.5\\ 6x=1.5\\ x=\0.25\\ \\x+4y=0.25+4\cdot0.2=\boxed{\1.05 }$