Suppose you have 28 coins that are all dimes and quarters. The total value of the coins is $5.35. Write a system of equations that models this situation and solve the system to find the number of quarters and dimes.

1) The system of equations that models this situation is given as follows

0.1·x + 0.25·y = 5.35...(1)

x + y = 28...(2)

2) The number of dimes = 11 dimes

The number of quarters = 17 quarters

Step-by-step explanation:

1) The given parameters are;

The numbers of quarters and dimes = 28

The total value of the coins = $5.25

Let x represent the number of dimes and y represent the number of quarters, and given that a dime = $0.1 and a quarter = $0.25, we have;

The system of equations that models this situation is given as follows

$0.1·x + $0.25·y = $5.35...(1)

x + y = 28...(2)

2) Making y the subject of both equations gives;

From equation (1), we have;

0.1·x + 0.25·y = 5.35

0.25·y = 5.35 - 0.1·x

y = 5.35/0.25 - 0.1/0.25·x = 21.4 - 0.4·x

y = 21.4 - 0.4·x

From equation (2), we have;

x + y = 28

y = 28 - x

Equating both equations to find the common solution, gives;

21.4 - 0.4·x = 28 - x

x - 0.4·x = 28 - 21.4

0.6·x = 6.6

x = 6.6/0.6 = 11

x =  11

The number of dimes = x = 11

y = 28 - x = 28 - 11 = 17

y = 17

The number of quarters = y = 17.