A collection of nickels and dimes is worth $4.40. There are 53 coins in all. How many nickels are there?

Nickel is a US coin worth 5 cents or 0.05.
Dime is a US coin worth 10 cents or 0.10

n + d = 53
0.05n + 0.10d = 4.40

n = 53 - d
0.05(53 - d) + 0.10d = 4.40
2.65 - 0.05d + 0.10d = 4.40
0.05d = 4.40 - 2.65
0.05d = 1.75
d = 1.75 / 0.05
d = 35

n = 53 - d
n = 53 - 35
n = 18

There are 18 nickels and 35 dimes.

0.05n + 0.10d = 4.40
0.05(18) + 0.10(35) = 4.40
0.90 + 3.5 = 4.40
4.40 = 4.40

4 0

3 years ago

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There are fifteen teams in a high school baseball league. How many different orders of finish are possible for the first four p

ankoles [38]

There are 32,760 different orders for the first four positions.

This is a permutation where repetition is not allowed; the formula for that is:

$_nP_r=\frac{n!}{(n-r)!}$

For our problem, we have:
$_{15}P_4=\frac{15!}{(15-4)!}=\frac{15!}{11!}=32760$

3 0

3 years ago