Answer:
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.
