If evan has 10 dimes and quarters in his pocket, and they have combined value of 190 cents, how many of each coin does he have?

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Answer 1 · 2016-10-24T01:54:36

6 quarters and 4 dimes.

To solve this problem in two variables (dimes and quarters) it is necessary to write two equations.

The first equation is dimes + quarters = #10#

The second equation is #0.10# x dimes + #0.25# x quarters =$ 1.90

Now it is clear then dimes = #10# - quarters so this value can be put into the second equation giving

#0.10 xx# ( 10 - quarters) + #0.25 xx# quarters = #$ 1.90#

#$1.90 = 190# cents.

This gives

#100# cent - #10# quarters + #25# quarters = #190# cents

Now #25# quarters - #10# quarters = #15# quarters.

so #15 quarters + #100# cents = #190# cents

now subtract #100# cents from both sides

#15# quarters + #100# cents - #100# cents = #190# cents - #100# cents

giving #15# quarters = #90# cents. It takes 6 quarters

If there are #6# quarters there must be only #4# dimes

#6 + 4 = 10#

#90# cents = #0.90#

# (0.90/.15 )xx (100/100 ) = 90/15 = 6 #

#6# quarters x #$0.25# /quarter = #$ 1.50#

#4# dimes x #$0.10# /dime = #$0.40#

                   Total   =        $1.90