Marcy has total of 100 dimes and quarters. If the total value of the coins is $14.05, how many quarters does she have?

2 Answers
Noah G
Sep 4, 2016

Marcy has #27# quarters.

Explanation:

Write a systems of equations.

Let #x# be the number of quarters, and #y# be the number of dimes.

#x + y = 100#

#0.25x + 0.10y = 14.05#

Solve by substitution:

#y = 100 - x#

#:.#0.25x + 0.10(100 - x) = 14.05#

#0.25x + 10 - 0.10x = 14.05#

#0.15x + 10 = 14.05#

#0.15x = 4.05#

#x = 27#

Solve for #y# now:

#y + 27 =100#

#y = 100 - 27#

#y = 73#

Hence, Marcy has #27# quarters and #73# dimes.

Hopefully this helps!

MeneerNask
Sep 4, 2016

If she had only dimes she'd have #$10.00#

Explanation:

Every time she substitutes one dime for a quarter, she adds #$0.15# to the total value. She has to add #$14.05-$10.00=$4.05#
So she will have to substitute #($4.05)/($0.15)=27# coins.

Answer: she has 27 quarters.

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