Alexa has some dimes and some quarters. she has a minimum of 28 coins worth a maximum of $5.05 combined. if alexa has 17 quarters, determine all possible values for the number of dimes that she could have. your answer should be a comma separated list of values. if there are no possible solutions, submit an empty answer.

There are no possible solutions

Step-by-step explanation:

Given:

Minimum number of coins Alexa has =28 coins

Number of quarters Alexa has = 17 quarters

Total amount in coins = $5.05 = 505 cents

Let number of dimes be = coins

So we can have two inequalities.

1) Total number of coins

 [Since minimum number of coins=28]

2) Total value of coins

[As 1 dime=10 cents and 1 quarter=25 cents]

Solving inequality (1)

Subtracting both sides by 17.

∴

Solving inequality (2)

Subtracting both sides by 425.

Dividing both sides by 10.

∴

On combining both solutions

and   ,

we see that there are no possible solutions as number of dimes cannot be ≥11 and ≤8 at the same time.

step-by-step explanation: