SOLUTION: How Do i Solve THe following Equation? Translate to a system of equations and solve. A collection of nickels and dimes totals $22.40. There are 304 coins in all. How many nick

Algebra ->  Algebra  -> Systems-of-equations -> SOLUTION: How Do i Solve THe following Equation? Translate to a system of equations and solve. A collection of nickels and dimes totals $22.40. There are 304 coins in all. How many nick      Log On

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Question 130316This question is from textbook Algebra 1
: How Do i Solve THe following Equation?
Translate to a system of equations and solve.
A collection of nickels and dimes totals $22.40. There are
304 coins in all. How many nickels are there.This question is from textbook Algebra 1

Answer by solver91311(12126) About Me  (Show Source):
You can put this solution on YOUR website!
Let's say we have n nickels and d dimes. That means that:

n+%2B+d+=+304, because that is the number of coins we have altogether.

A nickel is worth 5 cents, so the value of all of the nickels is 5n cents. Likewise, the value of all of the dimes is 10d.

Just because I don't like mucking about with decimal coefficients, let's change the total amount of money from $22.40 to 2240 cents.

Now we can say that 5n%2B10d=2240

We can re-state the first equation by solving it for either of the variables. Let's solve it for d: d=304-n

Now take this expression for d and substitute it into the second equation:

5n%2B10%28304-n%29=2240

5n-10n%2B3040=2240

-5n=2240-3040

-5n=-800

n=160

So there were 160 nickels.

Check the answer.

If there were 160 nickels, then there were 144 dimes (304 - 160). 144 dimes is $14.40, 160 nickels is $8.00. $14.40 + $8.00 = $22.40. Answer checks.