word probs: sum of 2 numbers 208; 1/3 larger equals smaller

[kianamalele]

I am super lame in algebra and I need some help in completing some questions. They are word questions and i need help on several of them i will post a couple at a time to not overwhelm the boards. I would greatly appriciate anyone's help in solving these word problems and I need to verify my work so please give verifciation on the solution as well. Thank you!!!

QUESTION #1: The degree measure of the angles of a certain triangle are consecutive evenintegers. What are the degree measures of the three angles?

QUESTION #2: The sum of two numbers is 208. One-third of the greater number equals the smaller number. What are the numbers?

QUESTION #3: The sum of two number is 133. Four times the smaller of the two numbers equals three times the greater number. Find the numbers.

 

[Loren]

Re: MORE WORD QUESTIONS

The degree measure of the angles of a certain triangle are consecutive evenintegers. What are the degree measures of the three angles?

Again, name stuff and write them down.

Let one of the angles of a triangle be named "x".

According to the problem, the measure of the three angles are consecutive even integers. Suppose we have the number 24. What is the next consecutive even integer? Did you say 26? Good. Now, what process went through your mind to get 26 from 24? Did you say "I added 2"? Okay. Using that process, name the second angle of the triangle, if the first angle is named x. Did you say x+2? Good.

We now know that we have names for two angles of the triangle. They are...

Let the measure of one angle of a triangle be called x.
The measure of the second angle is x+2.
The measure of the third angle is ???. Did you add 2 to the name of the second angle?

Now, use an idea about what you know about the sum of the angles of any and all triangles to write your equation. Solve your equation for x, then indicate the angle measurement for x, x+2 and x+4. Check your results back in the original word problem.

 

[fasteddie65]

QUESTION #2: The sum of two numbers is 208. One-third of the greater number equals the smaller number. What are the numbers?

Let n = the greater number and let n/3 equal the smaller number.
n + n/3 = 208
(4/3)n = 208
n = 156
n/3 = 52

QUESTION #3: The sum of two number is 133. Four times the smaller of the two numbers equals three times the greater number. Find the numbers.

Let m = the smaller number and let n = the larger number.

(1) m + n = 133
(2) 4m = 3n

(3) 4m - 3n = 0

Multiply the first equation by 3: 3m + 3n = 399

Now add this last equation to equation (3): 7m = 399
m = 57
n = 76