Word problem?

Question

I can't figure out this one please help!

 

The Miller family received 19 pieces of mail on February 10. The mail consisted of bills, magazines, letters, and ads. How many bills did they receive if they received the same number of bills as letters, three more magazines than letters, and five more ads than magazines?

Answer 1

Step 1:  First you must label individual items as variables from the word problem:

 

We know that we are searching for the number of bills received, so, 

• Let bills = (x)

 

And since we know that the Millers received the "same amount" of bills as letter, we  can label "letters" the same way as we labeled the "bills" (above), thus,

• Let letters (also) = (x)

 

Next, we know that the family received "3 more magazines than letters".  Since we determined that "letters = x" (above) we can now write that magazines are "x + 3" (3 more than x), thus,

• Let magazines = (x)+ 3

 

Lastly, since they received "5 more ads than magazines" and magazines are "x+3" (above), we can write the number of ads is equal to "x + 3 + 5", thus,

• Let Ads = (x + 3) + 5

Step 2:  Create an equation to solve for (x) (number of bills):

 

If we add all of the terms we created (above) together, the word problem states that we should have a total of 19 pieces of mail.  So, we must write out our equation, thus:

• (x) (# of bills) + (x) (# of letters) + (x + 3) (# of magazines) + (x + 3 + 5) (# of ads) = 19
• OR...simply...
• x + x + x + 3 + x + 3 + 5 = 19

 

Step 3:  Combine "like terms" in the equation to get:

• 4x + 11 = 19

 

*this was done by adding x + x + x + x on the left side only, to get 4x; then adding 3 + 3 + 5 on the left side only, to get 11; and then making the total of 4x + 11 equal to 19 pieces of mail (given in the word problem) on the right side.

 

Step 4:  Solve for "x" by isolating "x" on one side of the equation:

 

First, subtract 11 from both sides of the equation:

• 4x + 11 - 11 = 19 - 11, which gives the result of, 
• 4x = 8

 

Second, divide both sides of the equation by 4:

• 4x ÷ 4 = 8 ÷ 4, which gives the result of, 
• x = 2

*4x divided by 4 yield a 1x or just x...written either way is an acceptable answer.

 

The solution is therefore... x = 2!  

 

Plugging this number (x is equal to 2) back into the original variable that we created in Step for the "bills"...we now know that the Millers received 2 bills.

 

As an aside, we also know that they received 2 letters (letters also was equal to "x"), 5 magazines (x + 3 is the now known to be 2 + 3, which is equal to 5) and 10 ads (which was x + 3 + 5, or now known to be 2 + 3 + 5, which is equal to 10.

 

Hope this helps!

 

 

 

 

 

Answer 2

19 pieces of mail

 

b=# of bills

b=# of letters (same # of bills as letters)

b+3=# of magazines

(b+3)+5=# of ads

b+b+(b+3)+[(b+3)+5]=19

b+b+b+3+b+3+5=19

4b+11=19

4b=19-11

4b=8

b=2

2 bills, 2 letters, 5 magazines, 10 ads