Brianna has three times as much money as Julia. Julia has $12 more than Joseph. Together they have $113. Write an equation and solve. How much money does Brianna have? (only use one variable)

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# 3 Answers

We really want to get Briana's amount so call it B

Julia has B/3 and Joseph has B/3 -12

So alltogether they have 113 = B + B/3 + (B/3 - 12)

Breaking the parenthesis and arranging the equation we get B = $ 75

And looking at it using only one variable:

Let's say Brianna has x dollars. Then Julia has (1/3)(x), or x/3 dollars (1/3 as many x as Brianna). Joseph has 12 less than Julia, or (x/3)-(12) dollars. All three together have $113 dollars, so...

x + x/3 + (x/3)-12 = 113

Get x's alone on one side: x + x/3 + x/3 -12 +12 = 113 +12 (add 12 to both sides)

Simplify: x + 2x/3 = 125; Multiply each term on both sides by 3: (3)(x) + (3)(2x)/3 = (125)(3), or 3x + 2x = 375 [ (3)(2x)/3 = 2x, and (125)(3) = 375 ]

5x = 375; divide both sides by 5: 5x/5 = 375/5; x = 75, the number of dollars Brianna has :-)

The best way to go about this question is to give each person a variable. Let's call Brianna "B" and Julia "J" Since Joseph can't also be J, let's call him "S".

So we know that Brianna has 3 times as much money as Julia. We write this as B = 3 x J or just B = 3J

We also know that Julia has $12 more than Joseph. We write this as J = S + 12.

We also know they have $113 total. We write this as B + J + S = 113

Now, let's plug in what we know. B = 3J so B + J + S = 3J + J + S

J = S + 12 and we can subtract 12 from both sides to get S = J -12

so 3J + J + S = 3J + J + J - 12 = 5J -12 and we know this is equal to 113

so 5J-12 = 113. Add 12 to both sides to get 5J=125 and divide both sides by 5 to get J = 25.

But what are we looking for? How much money does **Brianna** have. So let's go back to B = 3 x J from the beginning and multiply 25 by 3 to get $75 as the amount Brianna has. You've got your answer!

## Comments

I forgot I can only use one variable

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