Container A and Container B were filled completely with chicken powder. The total mass of 1/3 of the chicken powder in Container B and 1/11 of the chicken powder in Container A was 570 g. If 5/11 of the chicken powder in Container A was poured out, the total mass of the chicken powder in both containers became 2.28 kg. How much chicken powder was in
(a) Container A in grams?
(b) Container B in grams?
amount in A --- x, amount in B ---- y
x/11 + y/3 = 570
3x + 11y = 18810
6x/11 + y = 2280 , (5/11 of x was removed, leaving 6x/11 )
y = 2280 - 6x/11
sub into 3x + 11y = 18810
3x + 11(2280 - 6x/11) = 18810
3x + 25080 - 6x = 18810
-3x = -6270
x = 2090
then y = 2280 - 6(2090)/11 = 1140
So container A had 2090 g, and container B had 1140 grams.
The bot is wrong with a solution 5 times as long as mine.
You can be sure that the bot will apologize for getting the wrong answer
and then simply repeat my solution , as if it were its own.
Let's see what it does .
I apologize for any errors in my previous response. Thank you for providing the correct solution. Your method is simpler and more efficient than mine.
To solve this problem, we can set up a system of linear equations using the given information. Let's break down the steps:
Let's assume the mass of the chicken powder in Container A is "x" grams and the mass of the chicken powder in Container B is "y" grams.
Step 1: Translate the given information into equations.
From the problem statement, we can gather the following information:
- 1/3 of the chicken powder in Container B + 1/11 of the chicken powder in Container A = 570g
- 5/11 of the chicken powder in Container A + the chicken powder in Container B = 2.28kg (which is equal to 2280g)
Step 2: Convert the fractions into a common denominator.
To make the fractions easier to work with, let's convert them into a common denominator. In this case, we can use 33 as the common denominator:
- (1/3) * y + (1/11) * x = 570g becomes (11/33) * y + (3/33) * x = 570g
- (5/11) * x + y = 2280g becomes (5/11) * x + y = 2280g
Step 3: Simplify the equations.
- (11/33) * y + (3/33) * x = 570g can be simplified to (11y + 3x)/33 = 570g
- (5/11) * x + y = 2280g remains the same
Step 4: Rewrite the equations in terms of a single variable.
To solve the system, we can rewrite one of the equations in terms of a single variable. Let's solve for y in terms of x from the first equation:
(11y + 3x)/33 = 570g
11y + 3x = 570g * 33
11y + 3x = 18810g
y = (18810g - 3x)/11
Step 5: Substitute the value of y into the second equation.
Now we can substitute the value we found for y into the second equation:
(5/11) * x + y = 2280g
(5/11) * x + (18810g - 3x)/11 = 2280g
Step 6: Solve for x.
Multiply both sides of the equation by 11 to eliminate the denominators:
5x + 18810g - 3x = 11 * 2280g
2x + 18810g = 25080g
2x = 25080g - 18810g
2x = 626g
Divide both sides of the equation by 2 to isolate x:
x = 313g
Step 7: Substitute the value of x into the expression for y.
Using the expression we derived for y, we can substitute the value of x found in the previous step:
y = (18810g - 3x)/11
y = (18810g - 3 * 313g)/11
y = (18810g - 939g)/11
y = 1791g
So, the chicken powder in Container A weighs 313 grams, and the chicken powder in Container B weighs 1791 grams.
Therefore, the answers to the questions are:
(a) There are 313 grams of chicken powder in Container A.
(b) There are 1791 grams of chicken powder in Container B.
Let's start by setting up some equations to represent the given information.
Let x be the total mass of chicken powder in Container A and y be the total mass of chicken powder in Container B.
From the first sentence, we know that:
1. Container A and Container B were filled completely with chicken powder.
This means that:
x + y = the total capacity of the two containers
Next, we are told that:
2a. The total mass of 1/3 of the chicken powder in Container B and 1/11 of the chicken powder in Container A was 570 g.
Since we don't know the actual amounts in each container yet, we can use algebra to represent this information. Let's start by finding 1/3 of the chicken powder in Container B. We can do this by multiplying y by 1/3:
(1/3)y
Similarly, we can find 1/11 of the chicken powder in Container A by multiplying x by 1/11:
(1/11)x
The total mass of these two amounts is given as 570 g:
(1/3)y + (1/11)x = 570
Now, we are told that:
2b. If 5/11 of the chicken powder in Container A was poured out, the total mass of the chicken powder in both containers became 2.28 kg.
First, let's find 5/11 of the chicken powder in Container A that was poured out:
(5/11)x
This means that the amount remaining in Container A is:
x - (5/11)x = (6/11)x
The total mass of chicken powder in both containers after this removal is given as 2.28 kg:
x + y - (5/11)x = 2280
Simplifying this equation by combining like terms, we get:
(6/11)x + y = 2280
Now, we have two equations with two variables (x and y) that we can solve simultaneously to find their values. Using the first equation, we can rewrite y in terms of x:
y = (total capacity of the two containers) - x
y = (1 - 1/3) * (total capacity of one container) - x
y = (2/3) * (total capacity of one container) - x
Substituting this expression for y into the second equation, we get:
(6/11)x + (2/3) * (total capacity of one container) - x = 2280
(1/11)x = (2/3) * (total capacity of one container) - 2280
Multiplying both sides by 11, we get:
x = (22/3) * (total capacity of one container) - 25080
Substituting this expression for x into the first equation, we can solve for y:
(22/3) * (total capacity of one container) - 25080 + y = (total capacity of the two containers)
y = (7/3) * (total capacity of one container) - 4056
Now, we have expressions for x and y in terms of the total capacity of one container. Let's set up one more equation to solve for this unknown quantity. From the first sentence, we know that both containers were filled completely with chicken powder, so we can say:
(total mass of one container) = (total capacity of one container) * (density of chicken powder)
Let's call the density of chicken powder "d." Then, we have:
x + y = 2 * (total capacity of one container) * d
Substituting our expressions for x and y into this equation, we get:
(22/3) * (total capacity of one container) - 25080 + (7/3) * (total capacity of one container) - 4056 = 2 * (total capacity of one container) * d
Simplifying this equation by combining like terms, we get:
(29/3) * (total capacity of one container) = 2 * (total capacity of one container) * d + 29136
Dividing both sides by (2 * d), we get:
(total capacity of one container) = (29/6) * d * (total mass of chicken powder in both containers) + 29136 / (2 * d)
Now, we can plug in the values we know:
- We were given that the total mass of chicken powder in both containers became 2.28 kg after some removals, so we can write:
(total mass of chicken powder in both containers) = 2280 g
- We were not given the density of chicken powder, so let's call it "d" for now.
Using these values, we get:
(total capacity of one container) = (29/6) * d * 2280 + 14568 / d
Now, we can solve for d using the information from 2a. The total mass of 1/3 of the chicken powder in Container B and 1/11 of the chicken powder in Container A was 570 g. We can rewrite this equation in terms of the total mass of chicken powder in one container by using the fact that the two containers were filled completely:
(1/3) * (total mass of chicken powder in one container) + (1/11) * (total mass of chicken powder in one container) = 570 / 2
(14/33) * (total mass of chicken powder in one container) = 285
(total mass of chicken powder in one container) = (33/14) * 285
(total mass of chicken powder in one container) = 682.5 g
Now that we know the density and total capacity of one container, we can solve for x and y using our expressions from earlier:
x = (22/3) * 682.5 - 25080 = 3195 g
y = (7/3) * 682.5 - 4056 = 1275 g
Therefore, the answers are:
(a) Container A had 3195 g of chicken powder.
(b) Container B had 1275 g of chicken powder.