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.

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