Lisa has 35 coins consisting of nickels and quarters amounting to $5.75. How many coins of each does she have?

n+q = 35 => n = 35-q......(1)

5n+25q = 575......(2)

Plug (1) in (2),

5(35-q)+25q = 575

=> 20q = 400

q = 20 quarters

n = 35-q = 15 nickels

Set up two equations

n + q = 35

0.05n + 0.25q = 5.75 (multiply all terms by 100 to get rid of the decimals)

5n + 25q = 575

____________

n + q = 35

5n + 25q = 575

Now you can do this by elimination or substitution. I would do substitution.

n + q = 35

n = 35 - q

Now substitute this into the other equation for n

5 (35 - q) + 25q = 575

175 - 5q + 25q = 575

175 + 20q = 575

20q = 400

q = 20

Now substitute back in to find how many quarters

n + q = 35

n + 20 = 35

n = 15

There are 15 nickels and 20 quarters

Hope this helps: B

Set it up as an algebra problem, where x is quarters and y is nickels. Based on the value of each, the equation would be:

.25x + .05y = 5.75

We also know that the total coins are 35, so the 2nd equation we can make is:

x + y = 35

Now solve for one or the other and substitute.

x = 35 - y

.25(35 - y) + .05y = 5.75

8.75 - .25y + .05y = 5.75

-.2y = -3

y = 15

Now we know we have 15 nickels. 35 coins total less 15 nickels makes 20 quarters. Now substitute them back in to check:

(15 * .05) + (20 * .25) = 5.75

It works!

Type …………. Qty …………. Cost …………. Total

Nickels …………. n …………. 0.05 …………. n * 0.05 = 0.05n

Dimes …………. d …………. 0.25 …………. d * 0.25 = 0.25d

Total …………. n + d …………. ----- …………. 5.75

The first 2 rows of the last column always add up to the third row in that column.

0.05n + 0.25d = 5.75

Given: Combination is 35 coins

Means: n + d = 35

You now have 2 equations.

0.05n + 0.25d = 5.75

n + d = 35

Solve the 2nd one for n.

n + d = 35

n = 35 - d

Replace n with 35 - d in the 1st one.

0.05n + 0.25d = 5.75

0.05(35 - n) + 0.25d = 5.75

1.75 - 0.05n + 0.25d = 5.75

0.2d = 4

d = 20

Plug this solved d value into n = 35 - d to solve for n.

n = 35 - d

n = 35 - 20

n = 15

ANSWER: She has 15 nickels and 20 dimes.

n + q = 35

.05n + .25q = 5.75

.05(35 - q) + .25q = 5.75

1.75 - .05q + .25q = 5.75

.2q = 4

quarters = 20

nickles = 35 - 20 = 15