Kelvin collected some local and foreign stamps. 2/3 of them were local stamps and the rest
were foreign stamps. After he gave away 5/6 of his local stamps and 125 foreign stamps, he
had 1/6 of his stamps left.
(a) How many stamps did Kelvin give away?
(b) What fraction of his stamps given away were local stamps?
.
(a) Kelvin gave away 5/6 of his local stamps and 125 foreign stamps, so he gave away a total of (5/6)*(2/3)*(total number of stamps) + 125 = (10/9)*(total number of stamps) + 125 stamps.
(b) Kelvin gave away 5/6 of his local stamps, so the fraction of his stamps given away that were local stamps is 5/6.
KEVIN! WHERES KEVIN?!?!?
Kevin!!!!!! Are you home?????? 🤣🤣🤣🤣🤣🤣🤣
fix or eschew the NLP routines!
If he started with x stamps, then he gave away
(5/6)*(2/3)x + 125 = (5/9)x + 125 stamps
that means
4/9 x - 125 = 1/6 x
x = 450
(a) 5/9 * 450 + 125 = 375
(b) 250/375 = 2/3
Although I see competent tutors here who were on Jiska (eg oobleck, mathhelper) the new automatic answer system seems to be a total disaster for the math, physics and chemistry questions that I am accustomed to helping with. More often than not the answers are incorrect but even if correct they are so brief that I can not imagine them being of any use to the student unless a cheater taking a test. This is just insane.
To find the number of stamps Kelvin gave away, we can follow these steps:
Step 1: Determine the total number of stamps Kelvin had initially.
Let's assume that the total number of stamps Kelvin had is denoted by "x".
Since 2/3 of the stamps were local stamps, we can calculate the number of local stamps as (2/3) * x.
The rest of the stamps were foreign stamps, so the number of foreign stamps is equal to (1 - 2/3) * x, which simplifies to (1/3) * x.
Step 2: Calculate the number of stamps Kelvin had left after giving some away.
Kelvin gave away 125 foreign stamps and 5/6 of his local stamps.
After giving away 5/6 of his local stamps, he had 1/6 of his original local stamps left.
Thus, the number of local stamps he had left is (1/6) * (2/3) * x.
The number of foreign stamps he had left is his original count of foreign stamps minus 125, which is (1/3) * x - 125.
Combining the local and foreign stamps left, we can express this as:
(1/6) * (2/3) * x + (1/3) * x - 125.
This should be equal to the amount of stamps he had left, which is also equal to 1/6 * x.
Step 3: Solve for x.
By setting up an equation and solving it, we can find the value of x, which represents the total number of stamps Kelvin had.
(1/6) * (2/3) * x + (1/3) * x - 125 = 1/6 * x.
To simplify the equation, we can multiply through the equation by 6 to eliminate the fractions:
2 * (2/3) * x + 2 * (1/3) * x - 750 = x.
Now, simplify the equation further:
(4/3) * x + (2/3) * x - 750 = x.
Combine the like terms:
(6/3) * x - 750 = x.
Simplify the fractions:
2x - 750 = x.
Subtract x from both sides:
x - 750 = 0.
Add 750 to both sides:
x = 750.
Therefore, the total number of stamps Kelvin initially had was 750.
(a) How many stamps did Kelvin give away?
To find the number of stamps Kelvin gave away, we need to subtract the number of stamps he had left from the initial total.
He had 1/6 of his original stamps left, which is (1/6) * 750 = 125 stamps.
So, Kelvin gave away 750 - 125 = 625 stamps.
(b) What fraction of his stamps given away were local stamps?
To find the fraction of stamps given away that were local stamps, we can divide the number of local stamps given away by the total number of stamps given away.
The number of local stamps given away is 5/6 of his initial number of local stamps, which is (5/6) * (2/3) * 750 = 250 stamps.
The total number of stamps given away is 625 stamps.
So, the fraction of stamps given away that were local stamps is 250/625, which simplifies to 2/5.
Therefore, 2/5 of Kelvin's stamps given away were local stamps.