Word Problem

Question

two common names for streets are Fourth Street and Main Street, with 16,534 streets bearing one of these names. There are 296 more streets named Fourth Street than Main Street. How many streets bear each name?

Answer 1

1st: Write down the important information in equation form.

        Total # of Streets = 16,534

        y = # of Fourth Streets 

        x = # of Main Streets

        -> Combine information into equation: x + y = 16,534 [Eq. 1]

 

        296 more Fourth than Main ---> y = x + 296  [Eq. 2]

 

2nd: Combine equations to solve for x.

        x + y = 16,534  --->  x + (x +296) = 16,534 [Combine like terms]

        y = x + 296             2x + 296 = 16,534       [Subtract 296 from both sides]

                                      2x = 16,238                 [Divide both sides by 2]

                                        x = 8,119

 

3rd: Plug value for x back into [Eq. 1]

       x + y = 16,534 

       x = 8,119                          

       --> 8,119 + y = 16,534 [Subtract 8,119 from both sides] 

                         y = 8,415

 

4th: Check answers. Plug x and y values into [Eq.1] and [Eq.2]

      x + y = 16,534 ---> 8,119 + 8,415 = 16,534  *Check

      y = x + 296  ---> 8,415 = 8,119 + 296       *Check

 

 

Main Street: 8,119

Fourth Street: 8,415

 

I hope this helped.

Update: I'm sorry, I realized that the format of the answer could cause some confusion, so I updated it.

                                                                        

Answer 2

This is simple. We just need to understand how to input the word problem into a formula. We are given 16,534 and then 296. Realize that it says fourth street = main street + 296. There is our formula, but let's create terms.

 

x = fourth street

y = main street

 

Now we have:

 

x = y + 296

From this, we create the next formula which involves 16,534. We know from the information we were given that the two streets plus 296 are 16,534 so we have:

 

 x + y + 296 = 16,534. 

 

From the first formula, we know what x is so we plug it in:

 

y + 296 + y + 296 = 16,534 

 

Now, let's solve for y. 

 

2y + 592 = 16,534

2y = 15,942

y= 7971

 

Now we know y so let's find x by inputting y into the first formula. We get:

x=y+296

x=7971+296

x= 8267

 

Now, we need to divide 296 by 2 which gives us 148. We add to each value of x and y, 148 to find the right numbers. We do this because 296 is the difference between the two and adding each by the same amount keeps it a 296 difference. These two final numbers will than be the numbers needed. There are other ways to do this as well, but from this, we get 

 

7971+148=8119

8267+148=8415