Help pls! Use truth tables to show the following are equivalent:
1 answer:
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Answer:
True Statements are -
B. In 3 months, Ted will have saved the same amount that Jude saved in 2 months.
D. The total amount of money Jude has saved is always $20 more than the total amount Ted has saved.
Step-by-step explanation:
Given - Ted and Jude are each saving money each month. After x months, the amount of money, in dollars, that Ted has saved is represented by the
equation T = 40x, and the amount of money that Jude has saved is represented by the equation J = 60x.
To find - Choose all of the statements that are true.
A. Each month, Jude saves two-thirds as much money as Ted saves.
B. In 3 months, Ted will have saved the same amount that Jude saved in 2 months.
C. The amount of money Jude saves each month is $20 more than the amount Ted saves each month.
D. The total amount of money Jude has saved is always $20 more than the total amount Ted has saved.
Proof -
Given that,
After x months,
Ted saved the amount of money, T(x) = 40x
Jude saved the amount of money, J(x) = 60x
Now,
In 1 month,
Ted saved money, T(1) = 40(1) = 40
Jude saved money, J(1) = 60(1) = 60
So,
In 1st month, Jude saved money 20 more than Ted saved.
Now,
In 2 month,
Ted saved money, T(2) = 40(2) = 80
Jude saved money, J(2) = 60(2) = 120
So,
In 2nd month, Jude saved money 40 more than Ted saved.
Now,
In 3 month,
Ted saved money, T(3) = 40(3) = 120
Jude saved money, J(3) = 60(3) = 180
So,
In 3rd month, Jude saved money 60 more than Ted saved.
So,
Option C is incorrect
Because
In 1st month, Jude saves is $20 more than the amount Ted saves
In 2nd month, Jude saves is $40 more than the amount Ted saves
Now,
In 1st month,
Ted saves = 40
and
= 26.67
So, Jude will save = 40 + 26.67 = 66.67
But Jude saves 60
So,
Option A is incorrect.
i.e. A. Each month, Jude saves two-thirds as much money as Ted saves.
Now,
We can see that,
In 3 months, Ted will have saved the money = 120
In 2 months, Jude will have saved the money = 120
So,
Option B is correct.
i.e. B. In 3 months, Ted will have saved the same amount that Jude saved in 2 months.
Also,
We can see that
In 1st month, Jude saved money 20 more than Ted saved.
In 2nd month, Jude saved money 40 more than Ted saved.
In 3rd month, Jude saved money 60 more than Ted saved.
So,
Option D is correct.
i.e. D. The total amount of money Jude has saved is always $20 more than the total amount Ted has saved.
∴ we get
True Statements are -
B. In 3 months, Ted will have saved the same amount that Jude saved in 2 months.
D. The total amount of money Jude has saved is always $20 more than the total amount Ted has saved.