Question

elijah has some dimes and some quarters. he has a minimum of 18 coins worth at most $3.60 combined if Elijah has 12 dimes determune the maximum number of quarters that he could have

Answer 1

We have the following:

let x number of dimes

let y number of quarters

`\begin{gathered} 0.10x+0.25y\ge3.6 \\ x+y\ge18 \end{gathered}`

Therefore,

`\begin{gathered} x=12 \\ 12+y\ge18 \\ y\ge18-12 \\ y\ge6 \\ 0.10\cdot12+0.25y\ge3.6 \\ 1.2+0.25y\ge3.6 \\ y\ge(3.6-0.12)/(0.25) \\ y\ge9.6 \end{gathered}`

Therefore, The quarters can range from 6 coins to 9.6 coins, that is, the maximum can be 10 coins.