math help?!?

Question

a collection of 40 dimes and nickels is worth $2.90 how many nickels are there?

Answer 1

ok...d=# of dimes and n= # of nickels;
money in dimes would equal .10 * number of dimes or .1d
money in nickels would equal .05 * # nickels 0r .05n
.10d + .05n = 2.90 {multiply by 100 to get rid of dec - 10d + 5n = 290; then divide through by 5 to get 2d + n = 58}
d + n = 40

now you have a system of equations to solve any way you want...this is my work:

d+n = 40 and so d = 40 - n. substitute this into the simplified equation 2d + n = 58.
2(40 - n) + n = 58
80 - 2n + n = 58
80 - n = 58
-n = - 22
n=22

now solve for d
d + n = 40
d + 22 = 40
d = 18

ck:
10(18) + 5(22) =
180 + 110 =
290

there are 22 nickels!

Answer 2

Let dimes be x and nickels y. Because we know that there are 40 nickels and dimes total, we can say "x + y = 40". Also, because we know the value of a nickel and dime as well as the total value of all the coins, we can say ".10x + .05y = 2.90", giving us two equations of x and y. When you have two variables, this is all you need to find their values, provided that the equations are not identical. Let's recap:

x + y = 40
.10x + .05y = 2.90

What we want to do now is get rid of one variable. To do this, we can multiply both sides of the second equation by 10. Since we do it to both sides, it's okay. That gives us these two equations:

x + y = 40
x + .5y = 29

Subtract the two equations.

.5y = 11

Solve for y.

y = 22

Plug this back into the original equation to solve for x.

x + 22 = 40
x = 18

There you have it. x = 18, y = 22.

Answer 3

12

Answer 4

I think there would be 30 nickels and 14 dimes. 30 nickels would make it worth $1.50, and 14 dimes would make it worth $1.40. Add $1.50 + $1.40 and you get $2.90.

Answer 5

This is a two-unknown problem, so we'll need two equations:
D+N=40
.1D+.05N=2.9

So..Let's make it easy and multiply both sides of the 2nd equation by 10.
D+.5N=29

Now, let's multiply it by -1...

-D-.5N=-29
And add the first equation...
D+N=40 which gives...
.5N=11
Divide both sides by .5 to get...
N=22.

Let's verify...Plug 22 back into the first equation:
D+22=40
Subtract 22 from both sides...
D=18

Does this work? Plug those values back into the 2nd equation:
.1*18+.05*22=2.9 - Check.

There are 22 nickles.

Orion