Final answer:
Jason has a total of 7 dimes. This conclusion is reached by setting up an algebraic system of equations based on the given values of coins and total money, solving for the number of dimes and using that to find the number of nickels.
Step-by-step explanation:
The subject of the student's question is mathematics, specifically an algebraic word problem. Jason must figure out the mix of dimes and nickels, where nickels are worth 5 cents each and dimes are worth 10 cents each, to total the value of $1.10 with 15 coins.
Let's define variables: Let x be the number of dimes and y be the number of nickels. The problem gives us two equations:
- x + y = 15 (since there are a total of 15 coins)
- 10x + 5y = 110 (since the total value of the coins is $1.10, converted to 110 pennies)
We can use the first equation to express y in terms of x: y = 15 - x. Substituting this into the second equation: 10x + 5(15 - x) = 110. Simplifying, 10x + 75 - 5x = 110, leading to 5x = 35.
Divide both sides by 5: x = 7. Jason has 7 dimes. By substitution in the first equation, y = 15 - 7 = 8. Therefore, he has 8 nickels.