Shehkar pulls 31 coins out of his pocket. each coin is either a dime or a quarter. if he has a total of 5.95, how many dimes does he have?

1 Answer
Sep 29, 2015

Answer:

#12# dimes (and #19# quarters)

Explanation:

Define
#color(white)("XXX")d = # number of dimes
#color(white)("XXX")q = # number of quarters

We are told:
[1]#color(white)("XXX")d+q=31#
[2]#color(white)("XXX")10d+25q=595#

Multiply [1] by #10#
[3]#color(white)("XXX")10d+10q=310#

Subtract [3] from [2]
[4]#color(white)("XXX")15q=285#

Divide [4] by #15#
[5]#color(white)("XXX")q=19#

Substitute #19# from [5] for #q# in [1]
[6]#color(white)("XXX")d+19=31#

Subtract #19# from both sides of [6]
[7]#color(white)("XXX")d=12#