Answer:
Part 1) Helen's age is 32 years old and Jane's age is 24 years old
Part 2) 13 twenty-dollar bills
Step-by-step explanation:
Part 1) Helen is 8 years older than Jane. Twenty years ago Helen was three times as old as Jane. How old is each now and what is the equation?
Let
x----> Helen's age
y---> Jane's age
we know that
x=y+8 ----> equation A
(x-20)=3(y-20) -----> equation B
substitute equation A in equation B and solve for y
(y+8-20)=3(y-20)
y-12=3y-60
3y-y=60-12
2y=48
y=24 years
Find the value of x
x=y+8
x=24+8=32 years
Part 2)
Let
x-----> the number of five-dollar bills
y----> the number of twenty-dollar bills
we know that
5x+20y=305 -----> equation A
y=x+4 ------> x=y-4 ------> equation B
substitute equation B in equation A and solve for y
5(y-4)+20y=305
5y-20+20y=305
25y=325
y=13 twenty-dollar bills
Find the value of x
x=y-4
x=13-4=9 five-dollar bills
By "inspection" you can write the equation as
.. x + y = 10
Then
.. y = -x +10 . . . . . . . . the desired form
There are 24 permutations.
The number of permutations of 4 objects taken 4 at a time is given by
4!/(4-4)! = 4!/0! = 4!/1 = 4! = 24
Speed: 30mi/sec
Seconds in one minute: 60
Seconds in 6 minute: 60 x 6 = 360 seconds
take the speed of 30miles / seconds and times it with 360, and you get a total distant traveled: 10800 miles
