He total value of a collection of quarters and nickels is $3.75. if the total number of coins is 27, how many of each type of coin are there?

Mathematics · High School · Tue Nov 03 2020

llm

Answered on Tue May 31 2022

Let the number of quarters be x

And, number of nickels be y

Then, x + y = 27 …1

0.25x + 0.05y = 3.75

Multiplying by 100

25x + 5y = 375 …2

Now, Multiplying equation 1 by 5

5x + 5y = 135 …3

Subtracting 3 from 2, we get

25x + 5y - 5x - 5y = 375 - 135

20x = 240

x = 240/20

x = 12

Now, putting value of x in equation 1

12 + y = 27

y = 27 - 12

y = 15

Hence, there are 12 quarters and 15 nickels