Question

Ms. Pacheco, Mr Edwards, and Mr Richards are three math teachers at turner middle school. Ms. Pacheco is three years older than Mr. Richards. Mr. Edwards is twice as old as Mr. Richards, The sum of Mr. Richards' age and Mr Edwards' age is 81. How old is each person.

Answer 1

First, establish what you already know to be true:

`P = 3 + R \\ E = 2R \\ R + E = 81`

You can use these equations to solve each other. Let's take the last one,
`R + E = 81`. Using the additive property of equality, we find that
`R = 81 - E`. We now know that Mr. Richard's age is 81 minus Mr. Edward's age. If we substitute this equation into the second one, we have
`E = 2(81 - E)`. Now use the distributive property to simplify:

`E = 162 - 2E`, and solve for
`E`:

`E = 162 - 2E \\ 3E = 162 \\ E = 54`.

Now we have a definite age. Use this to find the other two ages:

`R + 54 = 81 \\ R = 27`
and

`27 = 3 + P \\ -P + 27 = 3 \\ -P = -24 \\ P = 24`.

We now know that Ms. Pacheo is 24, Mr. Edwards is 54, and Mr. Richard's is 27! :D

Answer 2

Mr edwards = Mr r x 2
Mr r = Mr p - 3 = Mr e ÷ 2. Mr p = 30
Mr e + Mr r = 81. Mr e = 54
Mr p = Mr r + 3. Mr r = 27

Mr Edwards = 2(Mr p - 3)
Mr e = 2(mr p) - 6

Mr r = [2(Mr p) -6] ÷ 2
Mr r = [2( Mr r + 3) - 6] ÷ 2

2(Mr r) + (Mr p - 3) = 81
2(Mr p -3) + (Mr p - 3) = 81
3(Mr p - 3) = 81
3(Mr p) - 9 = 81. Hope this helps!!!
3(Mr p) + 9 = 81 + 9
3(Mr p) = 90
Mr p = 90 ÷ 3
Mr p = 30