John has t tapes and James has ten tapes more than John.
Then we add 10 to t and get t+10 tapes that James has.
Answer: James has t+10 tapes
b. John gives James 14 of his tapes.
So we subtract 14 from the number of tapes that John has,
so John now has t-14 tapes.
And we must add those 14 tapes to the number of tapes that James has.
So James now has t+10+14 tapes which is the same as t+24 tapes.
James now has twice as many tapes as john has.
So the t+24 tapes that James has must equal to 2 times the t-14 tapes
which John has. So we make this equation:
t+24 = 2(t-14)
write an algebraic expression to represent the amount eavh person has
We solve that equation:
We use the distributive principle on the right side to remove the
parentheses:
t+24 = 2(t-14)
t+24 = 2t-28
We add -2t to both sides
t+24 - 2t = 2t-28 - 2t
We combine like terms:
-t + 24 = -28
We add -24 to both sides
-t + 24 - 24 = -28 - 24
-t = -52
The coefficient of t on the left is -1
-1t = -52
We divide both side of the equation by -1
=
t = 52
John started out with 52 tapes and James started out with 10 more, or 62
Therefore John started out with 52, and James had t+10, or 52+10, or 62.
Then John gave James 14 tapes. Then John had 52-14 or 38 tapes left. And
James then had 62+14 or 76 tapes,
And if you multiply 38 by 2 you get 76.
Edwin