Question

A coin purse has only nickels and quarters in it. The total value of the coins is $1.05. Millie claims that there are 10 coins in the purse. Write and solve a system of equations for this situation

Answer 1

Assuming x = nickels,
y = quarters

$x + y = 10 \\ 0.05x + 0.25y = 1.05$

$x = 10 - y$
Substitute that into
$0.05(10 - y) + 0.25y = 1.05 \\ 0.5 - 0.05y + 0.25y = 1.05 \\ 0.2y = 0.55 \\ y = 2.75$

$x + 2.75 = 10 \\ x = 7.25$

Hope this helps. - M