2 Letters chosen among 6 with no repeat:
a) the first has 6 ways
the second has 5 ways
Then to choose 2 letters among 6, with no repeat, there are 6x5 = 30 ways
b) 3 numbers are taken from the digits 0 through 9 with repeats (total = 10)
the first has 10 ways
the second has 10 ways
the third has 10 ways
Then to choose 3 numbers among 10, with repeat, there are 10x10x10= 1000 ways
And the total serial numbers that can be generated is
30 x 1000 = 3000
let's say the bill without the tip is "x" amount, so that'd be the 100% of the bill, but we also know that 4.50 is the 18% of "x".
so if 4.50 is the 18% of "x", how much is "x"?
Answer:
Yes you did good job
Step-by-step explanation:
The value of the coin times the number of coins all added up equals the total value of the piggy bank
so
0.05n + 0.10d = 5.60
then they have given us "number of nickels is 8 less than 3 times the dimes"
this translates to
n = 3d - 8
we plug this into our first equation and we get
0.05(3d - 8) + 0.10d = 5.60
now we solve for d
first we can distribute the 0.05
0.15d - 0.40 + 0.10d = 5.60
then we can add the 0.15d and 0.10d together
and get
0.25d - 0.40 = 5.60
then we can add 0.40 to both sides
0.25d = 6.00
then divide both sides by 0.25
d = 6.00 / 0.25 = 24
so we have 24 dimes
then to find nickels, we plug in 24 for d into
n = 3d - 8
and get
n = 3(24) - 8
n = 72 - 8
n = 64
therefore we have
64 nickels
and
24 dimes
