Question

A coin bank contains nickels and dimes. The
number of dimes is 10 less than twice the
number of nickels. The total value of all
coins is $2.75. Find the number of each type
of coins in the bank. Show work

Answers

  1. Using a system of equations, it is found that there are 15 nickels and 20 dimes on the bank.

    What is a system of equations?

    A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
    In this problem, the variables are given by:
    • Variable x: Number of nickels.
    • Variable y: Number of dimes.
    He has an amount of $2.75 in coins, hence, considering the value of each coin:
    0.05x + 0.1y = 2.75
    The number of dimes is 10 less than twice the number of nickels, hence:
    y = 2x – 10.
    Replacing in the first equation:
    0.05x + 0.1(2x – 10) = 2.75
    0.05x + 0.2x – 1 = 2.75
    0.25x = 3.75
    x = 3.75/0.25
    x = 15
    y = 2x – 10 = 2(15) – 10 = 30 – 10 = 20.
    Hence there are 15 nickels and 20 dimes on the bank.
    More can be learned about a system of equations at https://brainly.com/question/24342899
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