Question

Beth has three as much money as Dennis. Dennis has $20 more than Will. If all of them had a total of $1260, how much money does Beth have?

Answer 1

Beth has $752

Explanation:

First we lay out what we know:

Beth: 3x+20

Will: x

Dennis: x+20

Next we write the equation:

3x+20+20+x+x=1260

Then we add any numbers that can be added to each other:

5x+40=1260

Then we solve,

We first minus 40 from both sides of the equation,

5x+40=1260

-40 -40

---------------------

5x=. 1220

Last we divide 1220 by 5,

5x=1220

÷5. ÷ 5

----------------

x=244

Now that we know that x is 244 we fill in the blanks,

Beth: 732+20

Will: 244

Dennis: 244+20

Then we just solve the equations,

Beth: 732+20=752

Will: 244

Dennis: 244+20=264

That's it,

if you want to check your work you can add them all up and if they equal 1260 it's correct.

752+244+264=1260

Your welcome, have a good day/night.

Answer 2

Let's use variables to represent the amounts of money each person has:

- Let x be the amount of money that Will has.
- Then, Dennis has $20 more than Will, so Dennis has x + $20.
- Beth has three times as much money as Dennis, so Beth has 3(x + $20).

We know that the total amount of money that all three have is $1260, so we can write an equation:

x + (x + $20) + 3(x + $20) = $1260

Simplifying and solving for x:

x + x + $20 + 3x + $60 = $1260
5x + $80 = $1260
5x = $1180
x = $236

So Will has $236, Dennis has x + $20 = $256 + $20 = $276, and Beth has 3(x + $20) = 3($256) = $768.

Therefore, Beth has $768.