Question

Trevor has $8 in savings and adds $1 each week. Aretha has $12 in savings and adds $3 each week. After how many weeks will Aretha’s account have twice as much as Trevor’s account?

Answer 1

@whpalmer4

Answer 2

Write some equations that reflect what you are told in the problem statement.

We could let the amount in Trevor's account be called T, and Aretha's account be A.

Trevor starts out with $8, and adds $1 each week. If we let \(x\) be the number of weeks, then Trevor has \[T = $8 + $1*x\]agreed?
Can you write the corresponding equation for Aretha's account?

Answer 3

After you've written the equation for Aretha's account, you need to set up an equation for finding the point at which Aretha's account has twice as much as Trevor's. That will be simply \[A = 2 * T\]Then you substitute the right hand side of the equation you found for \(A\) on the left side in place of \(A\), and the equation I gave you for \(T\) on the right side in place of \(T\). If the equation for \(A\) turned out to be \(A = $10 + $5*x\) (hint: it isn't), the result would be
\[$10 + $5*x = 2*($8 + $1*x)\]
Then you solve that equation for \(x\), which is the number of weeks it takes for Aretha's account to have twice as much as Trevor's. If you want, you could remove the $ signs from the equation; they won't appear in the final result and don't change the value.

Answer 4

so whats the answer... i truly dont understand this!

Answer 5

im guessing 7 but i really have clue

Answer 6

Trevor has \[T = 8+1x\] in his account after \(x\) weeks.

Aretha has \[A = 12 + 3x\] in her account after \(x\) weeks.

Agreed?

Answer 7

Hello?

Answer 8

yes

Answer 9

i agree so A=15x and T=9x

Answer 10

Okay, now we're trying to find the point in time at which \[A = 2T\] (Aretha's account has twice the value of Trevor's)

So, substituting:
\[12+3x = 2(8+1x)\]\[12+3x = 16 + 2x\]

Answer 11

do i need to find a common multiple or something.. idk what concept im missing here... ive been out of school for 11 years... im getting a headache

Answer 12

\[ 12 + 3x \ne15x\] except if \(x =1\)

Answer 13

You have to add like things:

\[12+3x = 16+2x\]Let's subtract \(2x\) from each side:
\[12+3x-2x = 16+2x-2x\]What do you get after you simplify that?

Answer 14

nvm im more confused now... im just going to guess...

Answer 15

no, do not guess.

Answer 16

What is 3x-2x?

Answer 17

If you have 3 x's and take away 2 x's, how many x's are left?

Answer 18

x

Answer 19

1x, right?
\[3x-2x=1x\]or more simply \(x\) (the 1 is implied)

So our left side becomes\[12+3x-2x=16+2x-2x\]\[12+x = 16 + 2x -2x\]Now looking at the right side, I hope it is obvious that \(2x-2x=0\), so it becomes
\[12 + x = 16\]Now we subtract 12 from each side:
\[12 + x - 12 = 16 - 12\]
\[x = 16-12\]\[x = 4\]

So after 4 weeks, if we did everything right, Aretha should have twice the balance in her account as Trevor. Let's check our work:

Trevor has 8 + 1x in his account after x weeks. x = 4:
Trevor has 8 + 1(4) = 8 + 4 = 12

Aretha has 12 + 3x in her account after x weeks. Again, x = 4:
Aretha has 12 + 3(4) = 12 + 12 = 24

24 = 12*2
so after 4 weeks, Aretha has twice as much in her account as Trevor.

Answer 20

that makes sense.. i just dont know how im going to explain to my nephew but i made an account so i can show him this

Answer 21

How old is your nephew?

Answer 22

14