I have question about 8th grade algebra

Question

Terry types twice as many words per minute as cecilia. Paige types 5 words per minute less then Terry. Reggie types 10 words per minute more than Terry. How many words per minute does each person type if the total number of words per minute that Reggie and Cecilia type equals the total number of words per minute that Terry and Paige type?

Answer 1

The best way to approach these types of questions is to translate the information into formula-form:

 

T = 2C (Terry types 2x as fast as Cecilia)

P = T - 5 (Paige types 5 WPM less then Terry)

R = T + 10 (Reggie types 10 WPM more than Terry)

 

R + C = T + P (The total number of WPM that Reggie and Cecilia type equals the total number of WPM that Terry and Paige type) 

 

To use the last equation, we need to substitute for each variable (R, C, T, P) to get only one variable in the equation. If we rewrite the first equation, we can represent everyone in terms of T:

 

T = 2C

C = 1/2T

 

R + C = T + P

(T + 10) + (1/2T) = T + (T - 5) 

 

Now we can solve for T:

1.5T + 10 = 2T - 5 (simplify)

1.5T = 2T - 15 (subtract 10 from both sides)

-0.5T = -15 (subtract 2T from both sides)

T = 30 (divide both sides by -0.5)

 

We now know that Terry types 30 WPM, and can use this information to solve for the others' typing speeds:

T = 30 WPM

C = 1/2(30) = 15 WPM
P = (30) - 5 = 25 WPM
R = (30) + 10 = 40 WPM

 

We can check our answers by plugging the above values into the equation below:

R + C = T + P

40 + 15 = 30 + 25

55 = 55 

Answer 2

Hi Chris,

 

There's an awful lot of information in this question that you have to sort out and translate the English into math:

 

According to the first sentence, if Cecilia types X words per minute, then Terry types 2X words per minute.

 

According to the second sentence, Paige types 2X - 5 WPM.

 

3rd sentence:  Reggie types 2X + 10 WPM.

 

4th sentence:  2X + 10 + X = 2X + 2X -5

 

Combine like terms--> 3X + 10 = 4X - 5

 

Get the X's and numbers on opposite sides of the equal sign--> 15 = X

 

So Cecilia = 15

 

Terry = 30

 

Paige = 25

 

Reggie = 40

 

Dan