Algebra 1 Word problem

Question

Francisca has a total of 10 coins in her pocket, all of the nickels and dimes. If the value of the coins is $0.85, how many dimes does she have? 

Answer 1

N+D =10

10N+10D = 100

5N +10D = 85

subtract

5N = 15

N =15/5 = 3 Nickels

D =10-3= 7 Dimes

Answer 2

https://youtu.be/9Cl2WwIJ2ZM

Algebra 1 Word problem:

Francisca has a total of 10 coins in her pocket.  All of them are nickels and dimes. If the value of the coins is $0.85, how many dimes does she have?

·        They told us we are working with Nickels and Dimes.

·        So, that's 2 unknowns or 2 variables, n and d.

·        They also told us:

o  a # total of 10

o  a $ total of $0.85

·        Since we have 2 unknowns, we need to set up a System of 2 Equations.

·        A System of 2 Equations helps us solve a problem with 2 Unknowns.

Let's set up our 2 equations for # and $.

·        For the # equation:

Let n = # of nickels

Let d = # of dimes

So, n + d = 10

·        For the $ equation, we have to assign "value" to each of the coins:

A nickel is worth 5 cents or $0.05

A dime is worth 10 cents or $0.10

·        They told us we have 5 cents, a certain # of times + 10 cents, a certain # of times, that = $0.85

So,                         $0.05n                              +        $0.10d                                          = $0.85

To solve this, we have to have just 1 unknown, meaning just 1 variable.

·        So, we describe one of the variables in terms of the other. But, which one?

·        Well, since they are asking for # of dimes, let's describe a nickel in terms of a dime.

·        Let's apply this in the simpler # equation:

So, n + d = 10

becomes n = 10 - d

·        So now, in our $ equation, we can just replace "n" with "10 - d", and then solve for d, which is the # of dimes!

$0.05n + $0.10d = $0.85

$0.05(10-d) + $0.10d = $0.85

$0.5 - $0.05d + $0.10d = $0.85

$0.50 + $0.05d = $0.85

$0.05d = $0.35

d = 7

Check this with the # equation:

n + d = 10

n + 7 = 10

n = 3

Does that make sense? Let's see:

3 nickels + 7 dimes = $0.85 ?

3($0.05) + 7($0.10) = $0.85

$0.15 + $0.70 = $0.85

$0.85 = $0.85