Gene G. answered • 02/15/16

Tutor

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Retired Electrical Engineer Helping People Understand Algebra

You can write two equations from the problem statement.

First assign variable names for the coins

d = the number of 10-cent coins (dimes)

n = the number of 5-cent coins (nickels)

The easy equation comes from the first statement. You can calculate the total value of the coins:

0.05n + 0.10d = 8.00

The second statement is more involved. Start by looking for things you can write expressions for, then look for how to put those expressions together.

"twice the number of 5-cent coins" is 2n.

"20 less than" that number is 2n-20.

The number of dimes is thus

d = 2n-20

This is a system of equations. Since one of our equations is "d = ...", we can substitute for d in the other equation.

0.05n + 0.10d = 8.00

Substituting 2n-20 for d:

0.05n + 0.1(2n-20) = 8

Solve for n:

0.05n + 0.2n - 2 = 8

0.25n = 8 + 2

0.25n = 10

n = 40

Substitute the value for n in either equation and solve for d.

The second equation looks easier to work with.

d = 2n-20

d = 2(40) - 20

d = 2(40) - 20

d = 60

Check:

0.05n + 0.10d = 8.00

0.05(40) + 0.10(60) = 8.00

2.00 + 6.00 = 8.00

8.00 = 8.00

The total number of coins is 100.