Question

Nell has a piggy bank full of dimes and nickels. She empties the bank and counts the coins. She counts 30

coins in all, with a total value of $2.90. Nell says she has 14 dimes and 16 nickels.
(a) Write a system of linear equations to represent the number of coins that Nell had in her piggy bank
and the total value of the coins.
(b) Determine whether Nell could have counted the number of dimes and nickels correctly. Show all your
work to prove whether she counted the coins correctly.

Answer 1

[a] A dime is worth 10 cents (0.10 dollars) and a nickel is worth 5 cents (0.05 dollars). If there are 30 coins in all, we can set up a linear equation in standard form to look like this:

30 - n = d

Since the total is 2.9, we can do the following:

{ 30 - n = d

{ .05n + .10d = 2.90

And our system is in bold

(where n is nickels and d is dimes, you could also use x and y if you wish)

[b] She could have counted the number of dimes and nickles correctly, but she did not. The number of nickles is 2 with there being 28 dimes.

Now, we will solve:

.05n + .10(30 - n) = 2.90

.05n + 3 - .1n = 2.9

3 - .05n = 2.9

3 = .05n + 2.90

.05n = 0.1

n = 2

(dimes is 30 - 2 = 28)

Have a nice day!

I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather