SOLUTION: Valerie has $1.30 in the bank. She has 4 fewer nickels than quarters. Write an equation to solve the problem. How many quarters does she have? How many nickels does she have?

Algebra ->  Customizable Word Problem Solvers  -> Coins -> SOLUTION: Valerie has $1.30 in the bank. She has 4 fewer nickels than quarters. Write an equation to solve the problem. How many quarters does she have? How many nickels does she have?      Log On

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Question 1153376: Valerie has $1.30 in the bank. She has 4 fewer nickels than quarters. Write an equation to solve the problem. How many quarters does she have? How many nickels does she have?
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
q quarters
n nickels
system%28q-n=4%2C25q%2B5n=130%29

system%28q-n=4%2C5q%2Bn=26%29
.
.

Answer by ikleyn(52879) About Me  (Show Source):
You can put this solution on YOUR website!
.

In this site, there is a huge bunch of coin problems.  See the lessons
    - Coin problems
    - More Coin problems
    - Solving coin problems without using equations
    - Kevin and Randy Muise have a jar containing coins
    - Typical coin problems from the archive
    - Three methods for solving standard (typical) coin word problems
    - More complicated coin problems
    - Solving coin problems mentally by grouping without using equations
    - Non-typical coin problems
    - Santa Claus helps solving coin problem
    - OVERVIEW of lessons on coin word problems
in this site.

You will find there the lessons for all levels - from introductory to advanced,
and for all methods used - from one equation to two equations and even without equations.

A convenient place to quickly observe these lessons from a  "bird flight height"  (a top view)  is the last lesson in the list.

Read them and become an expert in solution of coin problems.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Coin problems".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.


Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


Using two variables to solve the problem, as one of the other tutors did, almost always makes for more work. Furthermore, the instructions say to solve the problem by writing AN (one) equation.

So, given that the number of nickels is4 less than the number of quarters, let x be the number of quarters and x-4 the number of nickels. Then you have one equation that is easily solved to find the answer to the problem.

25%28x%29%2B5%28x-4%29+=+130

Note that if a formal algebraic solution is not required -- as in a competition where getting an answer fast is desirable -- the problem can be solved mentally with a few simple steps:

(1) Add 4 more nickels; now the total is 150 cents and the numbers of quarters and nickels are the same
(2) One quarter and one nickel makes 30 cents
(3) To make 150 cents, you need 150/30 = 5 groups of one quarter and 1 nickel; that means 5 quarters and 5 nickels
(4) Now take away the extra 4 nickels you added to get 130 cents using 5 quarters and 1 nickel.

ANSWER: 5 quarters and 1 nickel.