The sum of a number and seven, multiplied by four, is thirty six

Question

I want to learn how to do this

Answer 1

Jesus,

"Turn Word Equations to Equations" is a good tag. Here's how:

First, identify the quantities involved.

The problem talks about "the sum of a number and ...", so we know there's "a number".

 

Let n be "a number"

 

Second, translate the words into mathematical symbols.

 

translate "the sum of a number and seven" into

"x + 7"

translate "multiplied by four" into " *4 "

translate "is thirty-six" into " = 36 "

String them all together:

 

(x + 7)*4 = 36

!!! Not so fast, Edward A! Where did the parentheses come from, and why do they  matter?

 

I'll answer out of order--the parentheses matter because (x+7)*4 is NOT the same as x+7*4. You probably know that already, I know.

Where did they come from? I needed them, so that you and I would both see the same problem.

 

So how would you know to put in the parentheses in this case? good question. Often, if you see commas, they may be intended to separate things that should be separated. In this case, they've got a comma between the "seven" and the "multiplied by 4". That's a meager clue, but if you ask yourself whether this sentence sounds more like

"add a number to 7, AND THEN multiply by 4"---(x+7)*4

or 

"multiply 4 by 7, AND THEN add a number to it"---x+(7*4)

you'll probably conclude  that parentheses belong around (x+7). 

 

In fact, you can't always count on commas, but the main things is, you have to be vigilant, and recognize that it's important to know where parentheses are implied by the words. 

 

At this point, the Word Equation has been Turned into an Equation.

I turn it over to you for solution.

Answer 2

Hi Jesus!  The easiest way to do this is set it up as an algebraic equation.  That sounds complicated but it's really not!  What you're looking for here is the "number".  It's the only thing you don't know, so you mark that down as "x":

 

x

 

Then, you just assemble the rest of the equation based on what comes next in the sentence.  "The sum of a number and seven" means that you have to add 7 to the number "x", so:

 

x + 7

 

The next part of the sentence is "multiplied by four".  You can tell that this applies to the sum of "x + 7" because in the sentence, the word "sum" is the subject and the phrase "multiplied by four" is surrounded by commas, meaning it refers back to the subject of the sentence rather than just the nearest noun to it.  That's the trickiest part about word problems: you have to have a good grasp of grammar in order to set them up right!  For this problem, though, here's what comes next in the equation:

 

(x + 7) * 4

 

Putting "x + 7" in parenthesis here means that you'll multiply the sum of those two numbers by 4, which is what we want based on the word problem.  The last step in setting this up is making it a full equation with that last bit of sentence there, "is thirty six".  The word "is" in word problems usually means "equals", so:

 

(x + 7) * 4 = 36

 

Now you've got your whole equation, and you just solve for "x"!  Remember, the way to do this is to get "x" by itself on one side of the equals sign, so the first step here is dividing both sides by 4 (because whatever you do on one side of the equals sign you have to do on the other, too).  You want to divide by 4 because "(x + 7)" is being multiplied by 4 on its side of the equation, and in order to get rid of a number on one side, you have to do the opposite of whatever it's doing.  If it's multiplying, divide; if it's adding, subtract; and vice versa.  So:

 

(x + 7) * 4 = 36

       4             4

 

Which works out to:

 

x + 7 = 9

 

Note that you can drop the parenthesis around "x + 7" here because there is no longer anything modifying the sum of those two numbers; they're just on their own.  This frees you up to then subtract 7 from both sides, since 7 is being added to "x", and you want to get "x" by itself.  So:

 

x + 7 – 7 = 9 – 7

 

Which works out to your answer:

 

x = 2

 

Voila!  Let me know if you have any questions, and if you're interested in tutoring, let me know!