20 coins in nickels and dimes. Total value is $1.50

Answer 1

Let N represent nickels (5 cents) and D represent dimes (10 cents).

A and B are the numbers of each

5A + 10B = $1.50 = 150 (cents) (1)

A + B = 20 (coins) (2)

Solve the system of equations for A and B

Multiply (2) by -5 and add to (1)

5A + 10B = 150

-5A -5B = -100

0A + 5B = 50

5B = 50

Divide both sides by 5 to find B = 10 dimes

Use the found value of B in (2) (or (1)) to find

A + 10 = 20

Solve for A to find A = 10 nickels

Test: in (1) 5(A) + 10(B) = 150

use found values of A and B to see that

5(10) + 10(10 = 50+100 = 150 = $1.50.

Answer 2

Let N=number of nickels and D=number of dimes

Equation 1: N+D=20 (total number of coins)

Now for total value:

Equation 2: 1.50 = (0.05)N + (0.10)D

We now have two equations and two unknowns, so we can solve it:

Let's solve for D in equation 1:

N+D=20

N+D -N = 20 -N subtracting N from each side

D= 20-N

Now let's plug this expression for D into the other equation:

1.50 = (0.05)N + (0.10)D

1.5=.05N + .1 (20-N)

1.5=.05N + (.1)(20) +(.1)(-N) (expand out)

1.5= .05N +2 -.1N (multiply)

1.5=-.05N+2 (combining N terms together)

1.5-2=-.05N +2 -2 (subtract 2 from each side)

-.5=-.05N (combine like terms)

-.5/-.05 = -.05/-.05 *N (divide each side by -.05)

10 = N (divide out the number terms)

Now, take 10 and substitute into the first equation for N:

N+D=20

10+D=20

10-10+D = 20-10 (subtract 10 from each side)

D=10 (combine like terms)

Now check our answer:

N+D=20 (eq 1)

10+10=20 (substitute our answers for N and D)

20=20 CHECK!

Check second equation:

1.50 = (0.05)N + (0.10)D (Eq 2)

1.50 = (0.05)10 + (0.10)10 (substitute in for N and D)

1.50 = .50 +1.0 (multiply out)

1.50 = 1.50 CHECK!

Both equations are satisfied, so we know we have the right answers D=10, N=10

Answer 3

Hey B L,

Ok so you have a problem involving coins/cents - so it will be important to be careful with your decimals!

The first thing to do with these kinds of problems is to use the info you are given to write equations. then you can find a way to mathematically find your answer.

You know you have a total of 20 coins made up of some number of dimes (d) and nickels (n) so

20 = n + d

You know that the total value of all your coins is $1.50. Remember that dimes are 10 cents (0.10) and nickels are 5 cents (0.05).

$1.50 = 0.10(d) + 0.05(n)

So you have 2 equations with 2 variables, so you can use the more simple one to take out one of the variables.

20 = n + d

n = 20 - d

Now you can use this equation to have only one variable in the other equation. Then continue to simplify that equation.

$1.50 = 0.10(d) + 0.05(n)

$1.50 = 0.10(d) + 0.05(20 - d)

$1.50 = 0.10(d) + 1 - 0.05d

0.50 = 0.10d - 0.05d

0.50 = 0.05d

d = 10

Going back to your original equation -> 20 = n + d -> 20 = n + 10

n = 10

So you have 10 nickels and 10 dimes.

You can check your answer

(10)(0.05) + 10(0.10) = 1.50

0.5 + 1.0 = 1.50

Let me know if I can explain anything better!