Respuesta :
Answer:
11, 12.
Step-by-step explanation:
Let q represent number of quarters.
We have been given that Caroline has a maximum of 15 coins worth at least $2.85 combined. We are also told that Caroline has 3 dimes. This means that total coins are less than or equal to 15.
We can represent this information in an inequality as:
[tex]q+3\leq 15...(1)[/tex]
We are also told that the coins worth at least $2.85 combined. This means that the worth of all coins is greater than or equal to 2.85.
We know that each dime is worth $0.10 and each quarter is worth $0.25.
[tex]0.25q+3(0.10)\geq 2.85...(2)[/tex]
Now, let us solve our system of inequalities.
From 1st inequality, we will get:
[tex]q+3-3\leq 15-3[/tex]
[tex]q\leq 12[/tex]
From 2nd inequality, we will get:
[tex]0.25q+0.30\geq 2.85[/tex]
[tex]0.25q+0.30-0.30\geq 2.85-0.30[/tex]
[tex]0.25q\geq 2.55[/tex]
[tex]\frac{0.25q}{0.25}\geq \frac{2.55}{0.25}[/tex]
[tex]q\geq 10.2[/tex]
Upon combining our both inequalities, we will get:
[tex]10.2\leq q\leq 12[/tex]
This means that numbers of quarters would be greater than or equal to 10.2 and less than or equal to 12.
Since we cannot have 0.2 of a coin, therefore, Caroline could have 11 or 12 quarters.
