WORD PROBLEM. PLEASE HELP.

Question

the sum of the average number of times a man, a woman, and a one-year-old child cry each month is 56.7. a woman cries 3.9 more times than a man. the average number of times a one-year-old cries per month is 43.3 more than the average number of times combined that a man and woman cry. What is the average number of times per month that each cries ?

 

 

wUse 4-step method to solve. Round to the nearest tenth. 

Answer 1

Step 1 (Main Idea):

 

We are looking for the average number of times each of three types of people cry per month.

 

Step 2 (Details):

 

The three types of people are men, women, and 1-year-olds. Let's call the 1-year olds babies. We are given three relationships between the quantities we are asked to find.

 

Step 3 (Strategy):

 

Let's represent the averages for a man, woman, and baby by M, W, and B respectively.

 

In order of the three statements in the problem, you get three equations.

 

(1)    M + W + B = 56.7

 

(2)    W = M + 3.9

 

(3)    B = M + W + 43.3

 

We will solve the problem by solving this system of linear equations

 

Step 4 (How?):

 

Plug (3) into (1) to get

 

Rewrite (3) as M + W = B - 43.3 and plug it into (1) get

 

B - 43.3 + B = 56.7

 

2B = 100.0

 

B = 50.0

 

Now plug this into (1) to get.

 

(4)    M + W = 6.7

 

Plug (2) into (4) to get

 

M + M + 3.9 = 6.7

 

2M = 2.8

 

M = 1.4

 

Plug this into (2) to get

 

W = 1.4 + 3.9 = 5.3

 

You should double check these numbers by plugging them into the original system and convince yourself that they are correct.

 

We just solved the system. We interpret it as follows:

 

Men cry an average of 1.4 times per month.

Women cry an average of 5.3 times per month.

1 year-olds cry an average of 50.0 times per month.