Answer:
The number of dimes is 10
The number of quarters is 7
Explanation:
Lily has a currency worth $ 2.75 . According to the question it consist of dimes and quarters. There are 17 coins in number this include both dimes and quarters.
let the number of dime = a
let the number of quarter = b
The total number can be computed as
a + b = 17...................(i)
The total worth can be computed as follows :
1 dime = $0.10
1 quarter = $ 0.25
Total worth is
a × 0.10 + b × 0.25 = 2.75
0.1a + 0.25b = 2.75 ...................(ii)
a + b = 17.................(i)
0.1a + 0.25b = 2.75................(ii)
a = 17 - b
insert a = 17 - b in equation(ii)
0.1(17 - b) + 0.25(b) = 2.75
1.7 - 0.1b + 0.25b = 2.75
0.15b = 2.75 - 1.7
0.15b = 1.05
b = 1.05/0.15
b = 7
insert b=7 in equation(i)
a + b = 17
a + 7 = 17
a = 17 - 7
a = 10
The number of dimes is 10
The number of quarters is 7