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?

Question

3424 views around the world

You can reuse this answer
Creative Commons License

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