Word Problem - Number Problem, 3

Category: Algebra

"Published in Newark, California, USA"

A two digit number is three times the sum of its digits. If 45 is added to the number, the digits are reversed. Find the number.

Solution:

The given word problem above is about finding the value of a two digit number with special conditions. Let's analyze the given word problem above as follows:

Le x = be the value of a tens digit
     y = be the value of a ones digit

If the first statement says, "A two digit number is three times the sum of its digits.", then the working equation will be

If the second statement says, "If 45 is added to the number, the digits are reversed.", then the working equation will be

Substitute the value of x from the first equation to the above equation, we have

Substitute the value of y to either of the working equations, we have

Therefore, the value of a two digit number is 27.

  

Rate, Distance, Time - Problem, 4

Category: Algebra, Physics, Mechanics

"Published in Newark, California, USA"

Mr. Saldaña drove out to a place in the country at the rate of 40 miles per hour and came back the same way at the rate of 60 miles per hour. How far out did he drive if the entire trip took 7 hours?

Solution:

The given word problem is about the rate, distance, and time problem. Let's analyze the word problem as follows:

Let x = be the time of first travel at 40 miles per hour 
      y = be the time of return travel at 60 miles per hour

To understand more the word problem, it is better to illustrate the given word problem as follows 

 We know that

The first distance traveled by Mr. Sadaña is equal to his return distance because it is a round trip travel. The working equation for this statement will be equal to

The other working equation which is the total time traveled by Mr. Sadaña will be equal to

Substitute the value of x from the first equation to the above equation, we have

Hence, the return distance traveled by Mr. Sedaña will be equal to

Therefore, the total distance traveled by Mr. Sedaña is 

Word Problem - Painting

Category: Algebra

"Published in Newark, California, USA"

Oscar estimates that he and Eddie can finish painting their house in 6 days. After painting together in 4 days, Oscar got sick and Eddie had to continue the work alone. It took Eddie 5 more days to finish the job. How many days would it have taken him to paint the whole house alone?

Solution:

The given word problem is about work problem which is painting the house. If there are many people working in a certain job, then they can finished it in lesser time and if there are less people working in a certain job, then they can finished it in longer time. Let's analyze the word problem as follows:

Let x = be the number of days needed by Oscar to finish the painting alone
      y = be the number of days needed by Eddie to finish the painting alone

If the first statement says, " Oscar estimates that he and Eddie can finish painting their house in 6 days.", then the working equation will be

If the second statement says, "After painting together in 4 days, Oscar got sick and Eddie had to continue the work alone. It took Eddie 5 more days to finish the job.", then the working equation will be

Next, solve for the values of x and y using the system of solving two equations two unknowns as follows

Multiply the first equation by 2 and -3 at the second equation, we have

Add the two equations and x will be eliminated

Therefore, Eddie would have finished painting the house, alone, in 15 days.