Question

Translate to a system of equations and solve:Priam has a collection of nickels and quarters, with a total value of $9.30. The number of nickels is six less than three times the number of quarters. How many nickels and how many quarters does he have?

Answer 1

The value of a nickel is 5 cents

The value of the quarter is 25 cents

Since Priam has a total of 9.30 dollars = 930 cents, then

`5n+25q=930`

Simplify the equation by dividing all terms by 5

`\begin{gathered} (5n)/(5)+(25q)/(5)=(930)/(5) \\ n+5q=186\rightarrow(1) \end{gathered}`

Since he has 6 nickels less than 3 times the quarters, then

`n=3q-6\rightarrow(2)`

Substitute n in equation (1) by equation (2)

`(3q-6)+5q=186`

Add the like terms on the left side

`\begin{gathered} (3q+5q)-6=186 \\ 8q-6=186 \end{gathered}`

Add 6 to both sides

`\begin{gathered} 8q-6+6=186+6 \\ 8q=192 \end{gathered}`

Divide both sides by 8

`\begin{gathered} (8q)/(8)=(192)/(8) \\ q=24 \end{gathered}`

The number of quarters is 24

Substitute q by 24 in equation 2 to find n

`\begin{gathered} n=3(24)-6 \\ n=72-6 \\ n=66 \end{gathered}`

The number of nickels is 66

He has 66 nickels and 24 quarters