SOLUTION: Dave Bowers collects U.S. gold coins. He has a collection of 47 coins. Some are​ $10 coins, and the rest are​ $20 coins. If the face value of the coins is ​$700​, how many

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Question 1144064: Dave Bowers collects U.S. gold coins. He has a collection of 47 coins. Some are​ $10 coins, and the rest are​ $20 coins. If the face value of the coins is ​$700​, how many of each denomination does he​ have?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39630)   (Show Source): You can put this solution on YOUR website!
t of the $20 coins
47-t of the $10 coins


Solve for t.
Answer by ikleyn(52898)   (Show Source): You can put this solution on YOUR website!
.

            There are several different Algebra approaches.

            Two of them are presented below -- the most popular among beginner students.


                    One equation setup 

Let x be the number of the $20 coins.

Then the number of $20 coins is (47-x).


Then the "face value equation" is


    20x + 10*(47-x) = 700   dollars.


From the equation, express x and calculate


    x =  = 23.


ANSWER.  23 coins are the $20 coins and the rest 47-23 = 24  are the $10 coins. 


CHECK.   23*20 + 24*10 = 700 dollars.   ! Correct !


                    Two equations setup 

Let x be the number of the $20 coins, and

let y be the number of $10 coins.


From the condition, you have these two equations


    x  +   y =  47   coins       (2)

   20x + 10y = 700   dollars.    (3)


From the first equation, express  y = 47-x  and substitute it into the second equation.


You will get an equation for single unknown


    20x + 10*(47-x) = 700.      (4)


Equation (4) is identical to equation (1).
Therefore, the rest of solution is the same as in the first method, giving (of course) the same answer.


There are also other logical methods of solution without using equations -- see the lesson  (*)  in the list below.

All these methods are presented in the lessons
    - Coin problems
    - More Coin problems
    - Solving coin problems without using equations
    - Typical coin problems from the archive
    - Three methods for solving standard (typical) coin word problems (*)
    - Solving coin problems mentally by grouping without using equations
    - 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.


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