Answer:
Step-by-step explanation:
A dime is worth 10 cents. Converting to dollars, it becomes 10/100 = $0.1
A quarter is worth 25 cents. Converting to dollars, it becomes 25/100 = $0.25
Let x represent the number of dimes that Jayden has.
Let y represent the number of quarters that Jayden has.
Jayden has some dimes and some quarters. He has at most 25 coins. It means that
x + y ≤ 25
The coins worth at least $4.60 combined. It means that
0.1x + 0.25y ≥ 4.6 - - - - - - - - - - 1
If Jayden has 7 dimes, then
7 + y ≤ 25
y ≤ 25 - 7
y ≤ 18
Substituting x = 7 into equation 1, it becomes
0.1 × 7 + 0.25y ≥ 4.6
0.7 + 0.25y ≥ 4.6
0.25y ≥ 4.6 - 0.7
0.25y ≥ 3.9
y ≥ 3.9/0.25
y ≥ 15.6
All possible values for the number of quarters that he could have would be
15.6 ≤ y ≤ 18
