Final answer:
Subtract the value of 14 quarters ($3.50) from the total amount ($6.10) giving $2.60, which is the value of the dimes. Divide $2.60 by the value of one dime ($0.10) to find that the student has 26 dimes.
Step-by-step explanation:
To determine the number of dimes a student has if she had $6.10 worth of quarters and dimes and 14 quarters, we need to calculate the value of the quarters first. Each quarter is worth $0.25, so 14 quarters equal to 14 × $0.25 = $3.50. After subtracting the value of the quarters from the total amount, we get $6.10 - $3.50 = $2.60. This amount is in dimes. To find the number of dimes, divide the remaining amount by the value of one dime ($0.10): $2.60 / $0.10 = 26 dimes.