Question

Alexandra has 36 coins valued at $6.00. She has only nickels and quarters. Which equation can be used to solve for the number of nickels, n?

Answer 1

0.05n + 0.25(36 – n) = 6

Answer 2

Keywords:

Coins, nickels, quarters, equation, variables

For this case, we have 36 coins that represent 6 dollars. In addition, said coins are nickels and quarters. We must find an equation that can be used to find the number of nickels Alexandra has, of the 36 coins. For this, we must define two variables:

• n: Represents the number of nickels Alexandra has

• q: Represents the number of quarters Alexandra has

We know that:

$1\ nickel = 0.05\ dollars\\1\ quarter = 0.25\ dollars$

Thus, we have the following system of equations:

$0.05n + 0.25q = 6 (1)\\n + q = 36 (2)$

We clear "q" from the equation (2):

$q = 36-n$

We substitute "q" in equation (1):

$0.05n + 0.25 (36-n) = 6\\0.05n + 0.25 * 36-0.25n = 6\\0.05n + 9-0.25n = 6\\-0.20n + 9 = 6$

Thus, the equation that can be used to find the number of nickels Alexandra has is: $-0.20n + 9 = 6$

Answer:

The equation that can be used to find the number of nickels Alexandra has is: $-0.20n + 9 = 6$