Question

How do I setup this Systems of Equation?Azlyn has a collection of 61 nickels and quarters totaling $6.85. How many of each type of coin does he have?

Answer 1

Given that collection of nickels and quarters equals 61, thus;

`Let\text{ n represents nickels and q represents quarters}`
`n+q=61\ldots\ldots\ldots\ldots\ldots\text{equation 1}`

Also, 1 dollar is equal to 20 nickels;

Hence 1 nickel is 1/20 dollars = $0.05;

Similarly, 1 quarter is $0.25, thus;

`0.05n+0.25q=6.85\ldots\ldots\ldots\ldots\ldots\text{equation 2}`

Solving the two equations simultaneously;

`\begin{gathered} \text{From equation 1}, \\ n=61-q\ldots\ldots\ldots\ldots\ldots\ldots\text{.}\mathrm{}\text{equation 3} \\ \text{Put equation 3 in equation 2;} \\ 0.05(61-q)+0.25q=6.85 \\ 3.05-0.05q+0.25q=6.85 \\ 0.2q=6.85-3.05 \\ 0.2q=3.8 \\ q=(3.8)/(0.2) \\ q=19 \end{gathered}`
`\begin{gathered} \text{Put q=19 in equation 3;} \\ n=61-q \\ n=61-19 \\ n=42 \end{gathered}`

Hence, Azlyn has 42 nickels and 19 quarters