a cash register contains 165 coins consisting of pennies, nickles, and dimes. If the total number of nickels and dimes is equal to twice the number of pennies, and the total value of the coins is $7.95, find the number of each type of coin.

The number of

Pennies = 55 coins

Dimes = 38 coins

Nickels = 72 coins

Step-by-step explanation:

A penny is worth 1 cent. = 0.01p

A nickel is worth 5 cents = 0.05n

A dime is worth 10 cents = 0.10d

A cash register contains 165 coins consisting of pennies, nickels and dimes.

p + n + d = 165 coins

If the total number of nickels and dimes is equal to twice the number of pennies

n + d = 2p

We substitute

2p for n + d

p + n + d = 165 coins

p + 2p = 165

3p = 165

p = 165/3

p = 55 coins

n + d = 2p

n + d = 2(55)

n + d = 110

n = 110 - d

The total value of the coins is $7.95

0.01p + 0.05n + 0.10d = $7.95

We substitute

p = 55

n = 110 - d

0.01(55) + 0.05(110 - d) + 0.10d = 7.95

0.55 + 5.5 - 0.05d + 0.10d = 7.95

6.05 + 0.05d = 7.95

Collect like terms

0.05d = 7.95 - 6.05

0.05d = 1.9

d= 1.9/0.05

d = 38 coins

n = 110 - d

n = 110 - 38

n = 72 coins

The number of

Pennies = 55 coins

Dimes = 38 coins

Nickels = 72 coins

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

yess

step-by-step explanation:

idk whyy this is happening, i cant even read my notification bc i keep getting errors

~coco