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sandy has a total of 35 coins in her money jar is sandy's jar contains only nickels and dimes and the value of all the coins is $2.50, how many nickels does sandy have?

Verified Answer :

aj7911

0.05x + 0.10(35-x) = 2.50

Get rid of decimals by multiplying every term by 100:

5x + 10(35-x) = 250

5x + 350 - 10x = 250

-5x + 350 = 250

-5x = -100

x = 20 = the number of nickels.

The number of dimes is 35-x or 35-20 or 15 dimes.

Checking: 20 nickels is $1.00 and 15 dimes is $1.50

And indeed $1.00 + $1.50 = $2.50
Edwin

facundo3141592

By solving a system of equations we will see that Sandy has 20 nickels and 15 dimes.

How to solve a system of equations?

We need to define the variables:

  • x = number of dimes
  • y = number of nickels.

We know that there are 35 coins so:

x + y = 35

And the total values if $2.50, then:

x*$0.10 + y$0.05 = $2.50

Then our system is:

x + y = 35

x$0.10 + y*$0.05 = $2.50

To solve this, we need to isolate one of the variables in one of the equations. I will isolate x on the first equation:

x = 35 - y

Now we replace this on the other equation:

(35 - y)*$0.10 + y*$0.05 = $2.50

$3.5 - y*$0.05 =  $2.50

$3.50 - $2.50 =  y*$0.05

$1.00/$0.05 = y = 20

So there are 20 nickels and the other 15 coins are dimes.

If you want to learn more about systems of equations, you can read:

https://brainly.com/question/13729904

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