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

Answer:

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

$11\text{ and 12}$

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\frac{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;

$11\text{ and 12}$