Question

4. Four years ago, Melody was one fourth as old as her sister was then, In six years, Melody will be half as old as het sister will be then. Find their ages now.
5. The sum of the digits of a two-digit number is 12 . The value of the number is 6 less than 5 times the units digit. Find the number.
6. Hannah likes to spend her free time hanging out at the airport. She likes to run on the walkways. While running with the walkway, she can cover 48 feet in 3 seconds. While running against the walkway, she can cover 24 feet in 2 seconds. Find Hannah's rate (in feet per second) if the walkway stopped moving.

Answer 1

Answer:

4) Melody is 9 and her sister is 24

5) The numbers are 3 and 9

6) 14 feet per second

Step-by-step explanation:

Questions 4

There is a lot going on here.  This is probably hard to follow.  If it is, it is me and not you.

Let m = Melody and s = sister

m - 4 = 1/4(s-4)                     m + 6 = 1/2(s + 6)  Clear the fractions

4m - 16 = s -4                        2m -s = -6

Multiple the second equation by -1 and add together

4m - s = 12

-2m + s = 6

2m = 18  Divide both sides by 2

m = 9  Substitute this in to find the sister's age

2m + 12 = s + 6

2(9) +12 + s + 6

18 + 12 = s + 6

30 = s + 6  Subtract 6 from both sides

24 = s

Questions 5

x + y = 12              x = 5y - 6

Plug in 5y - 6 in the first equation for x

5y - 6 + y = 12  Combine like terms

6y - 6 = 12  Add 6 to both sides

6y = 18  Divide both sides by 6

y = 3

x + y = 12

3 + y = 12  Subtract 3 from both sides

y = 9

I am little confused by this because it says, "The value of the number..."  What number are they referring to?

Question 6

To find the rate taking into consideration the walkway rate:

$\frac{48}{3}$ - w  Which is equivalent to 16 - w

$\frac{24}{2}$ + w  Which is equivalent to 12 + w

Set these expression equal to each other and find the rate of the walkway

16 - w = 12 + w  Add w to both sides

16 = 12 + 2w  Subtract 12 from both sides

4 = 2w  Divide both sides by 2

2 = w

The rate of the walkway is 2 feet per second.  Subtract that from 16 or add is to the 12 to get 14 steps per second.