Question
A pile of coins, consisting of quarters and half dollars is worth $11.75. If there are 2 more quarters than half dollars, how many of each are there?
Answers
GPT 3.5
Let x be the number of half dollars
There are x+2 quarters
.50x+.25(x+2)=11.75
.50x+.25x+.50=11.75
.75x=11.25
x=<<15=15>>15 half dollars
There are 15+2 = <<15+2=17>>17 quarters. Answer: \boxed{15,17}.
There are x+2 quarters
.50x+.25(x+2)=11.75
.50x+.25x+.50=11.75
.75x=11.25
x=<<15=15>>15 half dollars
There are 15+2 = <<15+2=17>>17 quarters. Answer: \boxed{15,17}.
Violeta Legend
A pile of coins, consisting of nickels, dimes, and quarters is worth $4.55. There are 4 more dimes than nickels, and 3 more quarters than dimes. How many of each are there?
GPT 3.5
Let x be the number of nickels.
There are x + 4 dimes.
There are (x + 4) + 3 = x + 7 quarters.
The value of the nickels is .05x.
The value of the dimes is .10(x + 4) = .10x + .40.
The value of the quarters is .25(x + 7) = .25x + 1.75.
The total value of the pile of coins is .05x + .10x + .40 + .25x + 1.75 = 4.55.
Combining like terms, we get .40x + 2.15 = 4.55.
Subtracting 2.15 from both sides, we get .40x = 2.40.
Dividing both sides by .40, we get x = 6.
There are x + 4 = <<6+4=10>>10 dimes.
There are x + 7 = <<6+7=13>>13 quarters.
Thus, there are 6 nickels, 10 dimes, and 13 quarters. Answer: \boxed{6, 10, 13}.
There are x + 4 dimes.
There are (x + 4) + 3 = x + 7 quarters.
The value of the nickels is .05x.
The value of the dimes is .10(x + 4) = .10x + .40.
The value of the quarters is .25(x + 7) = .25x + 1.75.
The total value of the pile of coins is .05x + .10x + .40 + .25x + 1.75 = 4.55.
Combining like terms, we get .40x + 2.15 = 4.55.
Subtracting 2.15 from both sides, we get .40x = 2.40.
Dividing both sides by .40, we get x = 6.
There are x + 4 = <<6+4=10>>10 dimes.
There are x + 7 = <<6+7=13>>13 quarters.
Thus, there are 6 nickels, 10 dimes, and 13 quarters. Answer: \boxed{6, 10, 13}.
Violeta Legend
I spent 3/4 of my money, and then I spent 1/5 of what was left. What part of all my money did I spend?
GPT 3.5
To find the amount of money spent, you need to calculate the total amount spent, which is the sum of the amounts spent in each step.
Let's say you started with $100 (you can assume any amount for simplicity).
Step 1: You spent 3/4 of your money, so you spent 3/4 * $100 = $75.
Now, you have $100 - $75 = $25 left.
Step 2: You spent 1/5 of what was left, so you spent 1/5 * $25 = $5.
The total amount you spent is $75 + $5 = $80.
To find the part of all your money that you spent, you divide the total amount spent ($80) by the initial amount you started with ($100) and multiply by 100 to express it as a percentage.
Part spent = ($80 / $100) * 100 = 80%.
Therefore, you spent 80% of all your money.
Let's say you started with $100 (you can assume any amount for simplicity).
Step 1: You spent 3/4 of your money, so you spent 3/4 * $100 = $75.
Now, you have $100 - $75 = $25 left.
Step 2: You spent 1/5 of what was left, so you spent 1/5 * $25 = $5.
The total amount you spent is $75 + $5 = $80.
To find the part of all your money that you spent, you divide the total amount spent ($80) by the initial amount you started with ($100) and multiply by 100 to express it as a percentage.
Part spent = ($80 / $100) * 100 = 80%.
Therefore, you spent 80% of all your money.
Violeta Legend
I spent 3/4 of my money, then I spent 1/5 of what was left. What part of all my money do I have left?
GPT 3.5
To find the part of all your money that you have left, you need to calculate the remaining amount after each step.
Let's assume you started with $100 (you can assume any amount for simplicity).
Step 1: You spent 3/4 of your money, so you spent 3/4 * $100 = $75.
Now you have $100 - $75 = $25 left.
Step 2: You spent 1/5 of what was left, so you spent 1/5 * $25 = $5.
Now you have $25 - $5 = $20 left.
To find the part of all your money that you have left, you divide the remaining amount ($20) by the initial amount you started with ($100) and multiply by 100 to express it as a percentage.
Part left = ($20 / $100) * 100 = 20%.
Therefore, you have 20% of all your money left.
Let's assume you started with $100 (you can assume any amount for simplicity).
Step 1: You spent 3/4 of your money, so you spent 3/4 * $100 = $75.
Now you have $100 - $75 = $25 left.
Step 2: You spent 1/5 of what was left, so you spent 1/5 * $25 = $5.
Now you have $25 - $5 = $20 left.
To find the part of all your money that you have left, you divide the remaining amount ($20) by the initial amount you started with ($100) and multiply by 100 to express it as a percentage.
Part left = ($20 / $100) * 100 = 20%.
Therefore, you have 20% of all your money left.
Violeta Legend
I am F years old, and my brother is B years older. What was the difference of our ages two years ago?
GPT 3.5
Two years ago, you would have been F - 2 years old, and your brother would have been (F + B) - 2 years old.
The difference in your ages two years ago would be (F + B) - 2 - (F - 2), which simplifies to (F + B - 2 - F + 2), and further simplifies to B.
Therefore, the difference in your ages two years ago is B.
The difference in your ages two years ago would be (F + B) - 2 - (F - 2), which simplifies to (F + B - 2 - F + 2), and further simplifies to B.
Therefore, the difference in your ages two years ago is B.
Violeta Legend
Jilla ran at a speed of m miles per hour. How far did she run in t minutes?
GPT 3.5
To find how far Jilla ran in t minutes, you first need to convert t minutes to hours. Since there are 60 minutes in an hour, you divide t by 60 to get t/60 hours.
Next, you multiply the speed, m miles per hour, by the time in hours, t/60 hours.
Distance = Speed x Time
Distance = m miles/hour * (t/60) hours
This simplifies to:
Distance = (mt) / 60 miles
Therefore, Jilla ran (mt) / 60 miles in t minutes.
Next, you multiply the speed, m miles per hour, by the time in hours, t/60 hours.
Distance = Speed x Time
Distance = m miles/hour * (t/60) hours
This simplifies to:
Distance = (mt) / 60 miles
Therefore, Jilla ran (mt) / 60 miles in t minutes.
Violeta Legend
Wrong.
GPT 3.5
I apologize for the incorrect response.
To find the distance Jilla ran in t minutes, we need to convert the time from minutes to hours. Since there are 60 minutes in 1 hour, we divide t by 60 to obtain the time in hours: t/60.
Next, we multiply the speed, m miles per hour, by the time in hours, t/60, to find the distance: (m * (t/60)) miles.
Therefore, Jilla ran a distance of (m * (t/60)) miles in t minutes.
To find the distance Jilla ran in t minutes, we need to convert the time from minutes to hours. Since there are 60 minutes in 1 hour, we divide t by 60 to obtain the time in hours: t/60.
Next, we multiply the speed, m miles per hour, by the time in hours, t/60, to find the distance: (m * (t/60)) miles.
Therefore, Jilla ran a distance of (m * (t/60)) miles in t minutes.
Violeta Legend
Also wrong.
GPT 3.5
I apologize once again for the mistake. I misunderstood the question.
To find the distance Jilla ran in t minutes, we need to convert the time from minutes to hours by dividing t by 60. This gives us a time of t/60 hours.
Since Jilla's speed is given in miles per hour, we need to convert the time to hours in order to match the units.
Next, we multiply the speed, m miles per hour, by the time in hours, t/60, to find the distance in miles:
Distance = (m miles/hour) * (t/60) hours
This simplifies to:
Distance = (m * t) / 60 miles
Therefore, Jilla ran a distance of (m * t) / 60 miles in t minutes. Thank you for pointing out the error.
To find the distance Jilla ran in t minutes, we need to convert the time from minutes to hours by dividing t by 60. This gives us a time of t/60 hours.
Since Jilla's speed is given in miles per hour, we need to convert the time to hours in order to match the units.
Next, we multiply the speed, m miles per hour, by the time in hours, t/60, to find the distance in miles:
Distance = (m miles/hour) * (t/60) hours
This simplifies to:
Distance = (m * t) / 60 miles
Therefore, Jilla ran a distance of (m * t) / 60 miles in t minutes. Thank you for pointing out the error.
Violeta Legend
Good, that is right.
GPT 3.5
Thank you for confirming. I apologize for the initial mistakes, and I'm glad to have provided the correct answer. If you have any more questions, feel free to ask.
Violeta Legend
If the value of n nickels plus d dimes is c cents, what is n in terms of d and c?
GPT 3.5
To find the value of n in terms of d and c, we need to consider the value of each coin.
The value of a nickel is 5 cents, and the value of a dime is 10 cents.
So if we have n nickels, the value of those nickels would be 5n cents.
Similarly, if we have d dimes, the value of those dimes would be 10d cents.
According to the given information, the value of n nickels plus d dimes is c cents.
Therefore, we can write the equation: 5n + 10d = c.
To find n in terms of d and c, we can rearrange this equation:
5n = c - 10d
Dividing both sides of the equation by 5, we get:
n = (c - 10d) / 5
Thus, n is equal to (c - 10d) divided by 5, in terms of d and c.
The value of a nickel is 5 cents, and the value of a dime is 10 cents.
So if we have n nickels, the value of those nickels would be 5n cents.
Similarly, if we have d dimes, the value of those dimes would be 10d cents.
According to the given information, the value of n nickels plus d dimes is c cents.
Therefore, we can write the equation: 5n + 10d = c.
To find n in terms of d and c, we can rearrange this equation:
5n = c - 10d
Dividing both sides of the equation by 5, we get:
n = (c - 10d) / 5
Thus, n is equal to (c - 10d) divided by 5, in terms of d and c.
Violeta Legend
To sew tablecloths for the school dance, Mrs. Stitcher four more than three times as many yards of red fabric as gold fabric. If she bought a total of 112 yards, how many yards of each color did she buy?
GPT 3.5
Let's say Mrs. Stitcher bought x yards of gold fabric.
She bought four more than three times as many yards of red fabric as gold fabric, which can be expressed as 3x + 4.
The total amount of fabric she bought is the sum of the gold and red fabric, which is x + (3x + 4) = 112.
Combining like terms, we get 4x + 4 = 112.
Subtracting 4 from both sides, we get 4x = 108.
Dividing both sides by 4, we get x = 27.
Therefore, Mrs. Stitcher bought 27 yards of gold fabric and 3(27) + 4 = 85 yards of red fabric.
She bought four more than three times as many yards of red fabric as gold fabric, which can be expressed as 3x + 4.
The total amount of fabric she bought is the sum of the gold and red fabric, which is x + (3x + 4) = 112.
Combining like terms, we get 4x + 4 = 112.
Subtracting 4 from both sides, we get 4x = 108.
Dividing both sides by 4, we get x = 27.
Therefore, Mrs. Stitcher bought 27 yards of gold fabric and 3(27) + 4 = 85 yards of red fabric.
Violeta Legend
On her way to her grandmas house, J traveled three times as many miles by train as by bus. She traveled four times as many miles as by bus as by foot. If J traveled 34 miles in all, how many miles did she travel by train?
GPT 3.5
Let's say J traveled x miles by foot.
Then, J traveled 4x miles by bus.
And J traveled 3(4x) = 12x miles by train.
The total distance traveled is the sum of the distances traveled by foot, bus, and train:
x + 4x + 12x = 34
Combining like terms, we get 17x = 34.
Dividing both sides by 17, we get x = 2.
Therefore, J traveled 12x = 12(2) = 24 miles by train.
Then, J traveled 4x miles by bus.
And J traveled 3(4x) = 12x miles by train.
The total distance traveled is the sum of the distances traveled by foot, bus, and train:
x + 4x + 12x = 34
Combining like terms, we get 17x = 34.
Dividing both sides by 17, we get x = 2.
Therefore, J traveled 12x = 12(2) = 24 miles by train.