Question

The ratio of yellow paint to blue paint is 1:14. There are 180 bottles of yellow and blue paint in total. How many yellow and blue bottles of paint are there?
Answer
Please try again
Answer
180-77
Answer
Yellow paint plus blue paint equals 180 bottles of paint. There are 25 more bottles of blue paint than yellow paint. How many of each are there?
Answer
Give it another go
Answer
Please put in a different answer now
Answered by GPT 3.5
Let's call the common ratio between yellow and blue paint bottles "x."
We can set up a system of equations to represent the given information:
x * yellow paint = blue paint
Since the ratio of yellow to blue paint is 1:14, the equation is:
x * yellow paint = 14 * blue paint
Since there are 180 bottles of yellow and blue paint in total, the equation is:
yellow paint + blue paint = 180
Since we have two equations and two variables, we can solve for yellow paint and blue paint.
Let's substitute the first equation into the second equation to solve for the variables:
x * yellow paint + yellow paint = 180
Combining like terms, we get:
yellow paint * (x + 1) = 180
Dividing both sides by (x + 1), we get:
yellow paint = 180 / (x + 1)
Substituting this back into our original equation, we get:
x * yellow paint = 14 * blue paint
x * (180 / (x + 1)) = 14 * blue paint
Multiplying both sides by (x + 1), we get:
x * 180 = 14 * blue paint * (x + 1)
180 * x = 14 * blue paint * (x + 1)
Dividing both sides by 14 * (x + 1), we get:
(180 * x) / (14 * (x + 1)) = blue paint
Simplifying, we get:
(90 * x) / (7 * (x + 1)) = blue paint
Since blue paint is a positive integer, we need to find an integer x that makes this equation true.
The only integer value of x that makes this equation true is x = 2.
Substituting this value back into our earlier equations, we get:
yellow paint = 180 / (x + 1) = 180 / (2 + 1) = 180 / 3 = 60 bottles
blue paint = 14 * blue paint * (x + 1) = 14 * 60 = 840 bottles
So, there are 60 bottles of yellow paint and 840 bottles of blue paint. Answer: \boxed{60, 840}.
Answered by GPT 3.5
Let's call the ratio between yellow and blue paint bottles "x".
We know that the ratio of yellow to blue paint is 1:14, so we have:
Yellow paint = x
Blue paint = 14x
The total number of paint bottles is 180, so we can set up the equation:
Yellow paint + Blue paint = 180
x + 14x = 180
15x = 180
x = 180/15
x = 12
Therefore, there are 12 yellow paint bottles and 14 * 12 = 168 blue paint bottles.
Answered by GPT 3.5
180 - 77 = 103
Answered by GPT 3.5
Let's call the number of yellow paint bottles "x" and the number of blue paint bottles "y".

We know that the total number of paint bottles is 180, so we can set up an equation:
x + y = 180

We also know that there are 25 more bottles of blue paint than yellow paint, so we can set up another equation:
y = x + 25

Now we can solve this system of equations by substitution or elimination. Let's use substitution.

Substitute the expression for y from the second equation into the first equation:
x + (x + 25) = 180

Combine like terms:
2x + 25 = 180

Subtract 25 from both sides:
2x = 180 - 25
2x = 155

Divide by 2:
x = 155/2
x = 77.5

Since we can't have a fraction of a paint bottle, we need to round down to the nearest whole number. Therefore, there are 77 yellow paint bottles.

Now substitute the value of x into the second equation to find y:
y = 77 + 25
y = 102

Therefore, there are 77 yellow paint bottles and 102 blue paint bottles.
Answered by GPT 3.5
Let's call the number of yellow paint bottles "x" and the number of blue paint bottles "y".

We know that the total number of paint bottles is 180, so we can set up an equation:
x + y = 180

We also know that there are 25 more bottles of blue paint than yellow paint, so we can set up another equation:
y = x + 25

Now we can solve this system of equations by substitution or elimination. Let's use substitution.

Substitute the expression for y from the second equation into the first equation:
x + (x + 25) = 180

Combine like terms:
2x + 25 = 180

Subtract 25 from both sides:
2x = 180 - 25
2x = 155

Divide by 2:
x = 155/2
x = 77.5

Since we can't have a fraction of a paint bottle, we need to round down to the nearest whole number. Therefore, there are 77 yellow paint bottles.

Now substitute the value of x into the second equation to find y:
y = 77 + 25
y = 102

Therefore, there are 77 yellow paint bottles and 102 blue paint bottles.
Answered by GPT 3.5
Apologies for the confusion. Let's reevaluate the problem.

Let's call the number of yellow paint bottles "x" and the number of blue paint bottles "y".

We know that the total number of paint bottles is 180, so we have the equation:
x + y = 180

We also know that there are 25 more bottles of blue paint than yellow paint, so we have another equation:
y = x + 25

Now we can solve this system of equations.

Substitute the expression for y from the second equation into the first equation:
x + (x + 25) = 180

Combine like terms:
2x + 25 = 180

Subtract 25 from both sides:
2x = 180 - 25
2x = 155

Divide by 2:
x = 155/2
x = 77.5

Since we can't have a fraction of a paint bottle, we need to find a whole number value for x.

Let's try a different approach. We can observe that the difference in the number of blue and yellow bottles is constant at 25. To find a whole number value for x, we can try different values while keeping this difference of 25.

If x = 50, then y = 50 + 25 = 75
If x = 60, then y = 60 + 25 = 85
If x = 70, then y = 70 + 25 = 95
If x = 80, then y = 80 + 25 = 105

Based on these results, we see that when x = 70, y = 95.

Therefore, there are 70 yellow paint bottles and 95 blue paint bottles.