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# Write and simplify an expression to show how many quarters they have in all.

Charlie  has x quarters. Ty has 3 more quarters than Charlie has. Vinnie has 2 times as many quarters as Ty has.

### 3 Answers by Expert Tutors

Becca M. | Math with Becca - Energetic Tutor Specializing in MathMath with Becca - Energetic Tutor Specia...
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Hi!

Word problems are tricky for a lot of people. The first thing to do with word problems is figure out 1 - what you know, and 2 - what you need to know.

With this problem, we don't know much. We know that Charlie, Ty, and Vinnie have some quarters.

We need to find an expression to determine the quantity of quarters that they have.

(note: an expression is like a segment of a mathematical sentence, no equals or inequality sign. An equation is like a full mathematical sentence, including an equals or inequality sign)

The next step with world problems is assigning variables to unknowns.

X = Charlie's Quarters

T = Ty's Quarters

V = Vinnie's Quarters

There are words to look for in word problems that tell you which operation (addition, subtraction, multiplication, division) to perform. The phrase "in all" means to add all together. The word "more" means to add. and the word "times" means multiply.

So, we know that we need to add all of the boys' quarters together,

X + T + V

Whenever possible, we want to try and reduce the number of different variables. We have enough information in this problem to create an expression with 1 variable instead of 3.

We also know that Ty has THREE MORE quarters than Charlie. Since Charlie's quarters are represented by X, we add 3 to X to represent the quantity of quarters that Ty has. So, T = X+3.

If we plug in our new value for Ty, we get:

X+X+3+V

Now, we're down to two variables (X and V). We also know that Vinny has TWO TIMES as may quarters as Ty. We already know that Ty has X+3 quarters. If we remember that TIMES means to multiply, we can see that we need to multiply X + 3 by 2. X times 2 = 2X plus 3 timse 2 = 6. Vinny has 2X + 6 quarters. We can now plug in our new value for Vinny's quarters, we have:

X + X + 3 + 2X + 6

Now, we need to combine like terms. We add all the X's together: X + X + 2X = 4x. Then we add the numbers together. 3 + 6 = 9

The expression is 4x + 9

Hope this Helps!

Marnie D. | Math - wasn't a math whiz but was tutored and now I have a degree.Math - wasn't a math whiz but was tutore...
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C = Charlie,

T=Ty,

V=Vinnie,

X = Quarters

C = X (Charlie has X quarters)

T = X+3 (Ty has 3 more quarters than Charlie)

V = 2(X+3) or simplified 2(T) where T is the amount of quarters Ty has. Vinnie has twice as many quarters as Ty.

So, how many quarters do they have in all?  That implies adding the equations together:

(C +T +V);

X +(X+3) +2(X+3) simplify X+X+3+2X+6 simplify some more combining your X's,

4X+9 (this is how many quarters they  have in all)

To double check (optional), Substitute in an number for X representing quarters, let X =5;

C = 5, T=(5+3)=8, V=2(8)=16  so C+T+V = 5+8+16=29

and substitute 5 in for X in the expression, 4X+9 =4(5)+9=20 +9=29

I believe this is correct.  "more" usually implies addition, and "times" usually implies multiplication.  It says Ty has 3 more, not 3 times more, if I'm interpreting this correctly?  Sorry for this confusion whomever is asking the question, but it seems like it is reading differently for the other response?

Andy Z. | Economics and Math TutorEconomics and Math Tutor
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We know that the amount of quarters that Charlie has is x.

We know that the amount of quarters that Ty has is 3 more times as Charlie. Thus Ty has (x + 3) quarters.

We know that the amount of quarters that Vinnie has is 2 more times as Ty. Thus Vinnie has 2(x + 3) quarters, or 2x + 6 quarters

x + (x + 3) + (2x + 6) = 4x + 9

Thus we can conclude that Charlie, Ty, and Vinnie have a combined 4x + 9 quarters, where x = the number of quarters that Charlie has.

For example: Suppose that Charlie has 7 quarters, then our given information says that Ty has 3 more quarters than Charlie, which means that Ty has 10 quarters. Furthermore, Vinnie has 2 times the amount of quarters as Ty, which means that Vinnie has 20 quarters. Thus, the 7 quarters that Charlie has plus the 10 quarters that Ty has, and the 20 quarters that Vinnie has all total to 37 quarters between the three of them.

Using the formula that we derived (4x + 9) we can simply just plug in 7 for x and also get 37.