Question

Caroline has some dimes and some quaeters. she has a maximum of 15 coins worth at least $2.85 combined. if Caroline has 3 dimes determine all the possible values for the number of quarters she could have.

Answer 1

The possible values for the number of quarters she could have is;

`11\text{ and 12}`

Step-by-step explanation:

Given that Caroline has some dimes and some quarters.

she has a maximum of 15 coins worth at least $2.85 combined.

Let d and q represent the number of dimes and quarters she has.

1 dime = $0.10

1 quarter = $0.25

So, we have;

`\begin{gathered} d+q\leq15\text{ ----------1} \\ 0.10d+0.25q\ge2.85\text{ ------2} \end{gathered}`

if Caroline has 3 dimes;

`d=3`

substituting into equation 1 and 2;

`\begin{gathered} d+q\leq15 \\ 3+q\leq15 \\ q\leq15-3 \\ q\leq12 \end{gathered}`
`\begin{gathered} 0.10d+0.25q\ge2.85 \\ 0.10(3)+0.25q\ge2.85 \\ 0.30+0.25q\ge2.85 \\ 0.25q\ge2.85-0.30 \\ 0.25q\ge2.55 \\ q\ge(2.55)/(0.25) \\ q\ge10.2 \end{gathered}`

Therefore;

`10.2\leq q\leq12`

So the possible values for the number of quarters she could have is;

`11\text{ and 12}`