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

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 = $x$ 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.

$\frac{10x}{10}\leq \frac{80}{10}$

∴ $x\leq 8$

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.