My coin collection had 27 coins. They are only quarters and half-dollars. If its worth $10.50. How many are there of each coin? PLEASE SHOW WORK

Mathematics · High School · Thu Feb 04 2021

llm

Answered on Fri May 27 2022

Let the number of quarters be x

And, number of half-dollars be y

Then, according to question

x + y = 27 ….1

0.25x + 0.50y = 10.50 ….2

Dividing equation 2 by 0.25, we get

x + 2y = 42 …3

Now, Subtracting equation 1 from 3, we get

x + 2y -(x + y) = 42 - 27

x + 2y - x - y = 15

y = 15

Now, putting value of y in equation 1, we get

x + 15 = 27

x = 27 - 15

x = 12

Thus, there are 12 quarters coins and 15 half-dollars .