Question

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.

Answer 1

There are no possible solutions

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 =
`x` coins

So we can have two inequalities.

1) Total number of coins

`x+17\geq28\\` [Since minimum number of coins=28]

2) Total value of coins

`10x+(25)(17)\leq505` [As 1 dime=10 cents and 1 quarter=25 cents]

`10x+425\leq505`

Solving inequality (1)

Subtracting both sides by 17.

`x+17-17\geq28-17`

∴
`x\geq 11`

Solving inequality (2)

Subtracting both sides by 425.

`10x+425-425\leq505-425`

`10x\leq 80`

Dividing both sides by 10.

`(10x)/(10)\leq (80)/(10)`

∴
`x\leq 8`

On combining both solutions

`x\geq 11` and
`x\leq 8` ,

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