Shelly and kristen share a birthday, but shelly is 5 years older.
a. make a table showing their ages every year, beginning when kristen was born.
b. if kristen is 16 years old, how old is shelly?
c. if kristen is k years old, how old is shelly?
d. if shelly is s years old, how old is kristen?

Answer with explanation:

Given : Shelly and Kristen share a birthday, but Shelly is 5 years older.

i.e. Age of Shelly = Age of Kristen +5

a. Table show their ages every year, beginning when Kristen was born. :

 Kristen                        Shelly

  0                                    5

  1                                     6

  2                                    7

  3                                    8

  4                                    9

b. If Kristen is 16 years old, then the age of Shelly = 16+5=21

c. If Kristen is K years old,  then the age of Shelly = K+5

d. Also, age of Kristen = Age of Shelly - 5

If Shelly is S years old,  then the age of Kristen = S-5

Answer with Step-by-step explanation:

We are given that Shelly and Kristen share  a birthday

Let x be the age of Kristen and y be the age of Shelly.

Age of Shelly=

a.We have to make a table  showing ages of Shelly and Kristen.

Suppose, Kristen was born in year 2000.

x=0 then y=5

Now, the age of Shelly  and Kristen increases by every year  by 1.

b.If age of Kristen=16 years

We have to find the age of Shelly

Substitute x=16

years

c.Age of Kristen =K years

We have to find the age of Shelly.

Substitute x=K

Then, we get

Age of Shelly= years

d.Age of Shelly=S years

We have to find the age of Kristen.

Substitute y=S then we get

Hence, age of Kristen= years

For this type of problems, we try to work with the rate of production per unit time.

Let
x=rate of production of old machine (parts/hour)
x+2=rate of production of new machine  (parts/hour)

"the new machine finished a certain job in 7 hours while the old one needed 8 hours to produce the same number of engine parts. "  
means
7(x+2) = 8x
Solve for x
8x-7x=14
x=14 parts/hour (rate of old machine)
x+2=16 parts/hour (rate of new machine)

Check:  7(14+2)=112, 8(14)=112  ✔