Question

A collection of nickels and quarters has a total value of three dollars and contains 32 coins. Which of the following systems of equations could be used to find the number of each coin?

Answer 1

Answer:

$N + Q = 32$ and $.05N + .25Q = 3.00$

Step-by-step explanation:

Given that there is a collection of nickels and quarters.

Let N be the number of coins of nickels and

Q be the number of coins of quarters.

It is given that total number of coins are 32.

Number of coins of nickels + Number of coins of quarters = 32

$\therefore \bold{N+Q=32}$ is the first equation.

Now, we know that value of a one quarter coin is 25 cents or $\ \frac{25}{100} = \ 0.25$

and value of a one nickel coin = 5 cents = $0.05

Total value of all nickel coins = Number of nickel coins $\times$ value of one nickel coin = $.05N$

Similarly,

Total value of all quarter coins = Number of quarter coins $\times$ value of one quarter coin = $.25Q$

Total value of coins is 3 dollars.

$\therefore \bold{.05N + .25Q = 3.00}$ is the second equation.

So, the answer is:

$N + Q = 32$ and $.05N + .25Q = 3.00$