A jar contains n nickels and d dimes. There are 20 coins in the jar, and the total value of the coins is 1.40. How many nickels and dimes are in the jar

Question

How do you first set up a linear equation and then how do you slolve it?

Answer 1

Here's what we know:

n + d = 20 (there are a total of 20 nickels and dimes)

.05n + .1d = 1.4 (total change equals $1.40)

 

There are a couple of ways to solve this. You can go the elimination method by multiplying the second equation by an amount to get rid of a variable, or we can go substitution by isolating a variable in the first equation. I'll go with elimination in this case:

 

-10(.05n + .1d = 1.4) this will cause the d-variable to equal 0:

 n  +  d = 20

-.5n - d = -14

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.5n = 6

n = 12

 

Now that we know n, we can solve for d:

12 + d = 20

d = 8

 

Check:

.05 * 12 + .1 + 8 = 1.4

.6 + .8 = 1.4

1.4 = 1.4