Alice gave bill 15 more of her tapes out of x, while bill had 10 already. what is the value of x

Question

Alice has x tapes and Bill has 10 more tapes than Alice. Alice gives Bill 15 more of her tapes. Bill now has twice as many tapes as Alice now has. Write an algebraic equation to show this data and find the value of x.

 

Answer 1

Hi Shelcia;

Alice has x tapes and Bill has 10 more tapes than Alice. Alice gives Bill 15 more of her tapes. Bill now has twice as many tapes as Alice now has.

A=x

B=x+10

Then...

A=x-15

B=x+10+15=x+25

B=2A

We want only the variable of x...

Let's begin with...

B=2A

Let's substitute A with x-15...

B=2(x-15)

Let's substitute B with x+25...

x+25=2(x-15)

Let's distribute...

x+25=2x-30

Let's isolate x...

Let's subtract x from both sides...

-x+x+25=2x-30-x

25=x-30

Let's add 30 to both sides...

30+25=x-30+30

55=x

 

Alice has x tapes and Bill has 10 more tapes than Alice. Alice gives Bill 15 more of her tapes. Bill now has twice as many tapes as Alice now has.

Alice=55 tapes

Bill=55+10=65 tapes

Then...

Alice=55-15=40

Bill=65+15=80

 

2(A)=B

2(40)=80

80=80

Answer 2

Sheicia:

 

Let's look at this problem step by step.

 

 

At the start, Alice has x tapes.  Bill has x+10 tapes (in other words, "10 more tapes than Alice").

 

Once Alice has given Bill 15 of her tapes, Alice now has x-15 tapes remaining (15 less tapes than she started with), while Bill has x+10+15 or x+25 tapes (15 more tapes than he started with).

 

We also know that after Alice has given 15 tapes to Bill, Bill ends up with twice as many tapes as Alice.   This can be expressed algebraically as follows:

x+25=2(x-15)

 

We can now solve for x:

x+25=2x-30

25+30=2x-x

55=x

x=55 (Answer)

 

This can be checked by plugging 55 in for x in the Algebraic expression, to see if both sides match:

x+25=2(x-15)

55+25=2(55-15)

80=80 (CHECK)

 

Let me know if you have any questions.

 

George T.

Answer 3

Alice = x

Bill = x + 10

 

Alice after giving 15 away

x - 15

 

Bill after receiving 15

x+10+15 = x + 25

 

Bill now has 2 times what Alice has:

 

2(x-15) = x + 25

 

2x - 30 = x + 25

 

2x - x = 25 + 30

 

x = 55

Alice started with 55 tapes.

 

Double-check:

Bill had 65.

 

Alice gave away 15.

She then had 40 and Bill had 80.

 

So bill had twice as many as Alice had.  Correct.