Math help for SAT?

Question

a jar of 400 coins consists of only pennies, nickles, and dimes with a face value of $17. *the number of pennies equals the sum of nickles and dimes.* how many of each type of coin are in the jar?

Answer 1

Let's represent the number of pennies with P, number of nickels with N, and number of dimes with D.

You have a total of 400 coins, so:
P + N + D = 400.

The total value of the coins is $17, or 1700 cents. A nickel is worth 5 pennies, a dime is worth 10 pennies. So:

P + 5N + 10D = 1700.

Then we have the number of pennies equals the sum of nickels and dimes, so:

P = N + D.

Now we can solve the equations. Substitute P in the first two equations:

(N + D) + N + D = 400
(N + D) + 5N + 10D = 1700

Simplify the 1st one:
2N + 2D = 400
N + D = 200
N = 200 - D

Simplify the 2nd one:
6N + 11D = 1700

Substitute the 1st equation in the second:
6(200 - D) + 11D = 1700
1200 - 6D + 11D = 1700
5D = 500
D = 100

Fill this in in the 1st equation:
N = 200 - D = 200 - 100 = 100.

Finally we can fill this in in the 3rd equation:
P = N + D = 100 + 100 = 200.

So we have 200 pennies, 100 nickels and 100 dimes in the jar.

Answer 2

ok, so you know that the 400 coins have to equal 17 dollars, but the number of pennies have to equal the sum of your dimes and nickels.

p=n+d

400=p + n +d

Break that down and try some numbers. if you have 200 pennies, you'd have to also have 100 nickels and 100 dimes. See if that works.

200=100+100

400=200+100+100

but you also have to have them all add up to 17 dollars. So find out if it works.

200 pennies = 2 dollars
100 nickels = 5 dollars
100 dimes = 10 dollars

10+5+2=17

Answer 3

P + N +D =400
P= N + D
.01P +.05N + .1D= 17

Substitute P for N+D inthe first gettig 2P=400, so P= 200
Now substitute P=200 into the 2nd and 3rd equations getting:
N+D = 200 or N= 200-D
2+.05N +.1D = 17 or .05N+.1D =15 or
N+2D = 300
Substitute 200-D for N getting:
200-D+2D =300
D =100
So N =100
So there are 200 pennies, 100 nickles and 100 dimes.

Answer 4

400=p+n+d
17.00=.01p+.05n+.1d
p=n+d

Solve this system of equation by first substituting p into the first two equations:

400=(n+d) + n + d
17.00=.01(n+d) + .05n+.1d

Simplify:

400=2n+2d
17.00=.01n+.01d+.05n+.1d=.06n+.11d (*)

Solve for n in the first equation:

400-2d = 2n (divide by sides by 2)

So n = 200 - d Substitute this into (*)

17.00=.06(200-d)+.11d
17.00=12.00-.06d+.11d
17.00=12.00+.05d
5.00=.05d
d=100 so you have 100 dimes

n=200-d so n = 100 you have 100 nickels

400=p+n+d
400=p+100+100 so p=200 you have 200 pennies

Answer 5

200 pennies
100 nickels
100 dimes