7 pints of blue paint mix with 4 pints of yellow paint.
If you want to use a total of 44 pints, how many pints of blue paint and yellow paint will you have?
I am a parent trying to help my daughter with the question above. am lost please show me what to do use different numbers if you have to. thank you for your time
7 + 4 = 11 pints
You could use a proportion.
7/11 = x/44
Cross multiply and solve for x.
11x = 308
x = 28 pints of blue paint
Do the same for the yellow paint.
To solve this problem, we can set up a proportion using the given information.
Let's use different numbers to illustrate the process. Suppose we have 10 pints of blue paint and 6 pints of yellow paint. We want to find out how many pints of blue and yellow paint we will have if we use a total of 20 pints.
We can set up the proportion as follows:
(blue paint)/(yellow paint) = (total blue paint)/(total yellow paint)
Using the numbers from above, we get:
10/6 = (10+x)/(6+y)
Now, let's apply this to the original problem:
(blue paint)/(yellow paint) = (total blue paint)/(total yellow paint)
7/4 = (7+x)/(4+y)
We are given that the total amount of paint used will be 44 pints, so we can set up another equation:
(blue paint + yellow paint) = total paint
7 + 4 = 44
Now we have two equations and two variables. We can solve this system of equations to find the values of x (the additional pints of blue paint) and y (the additional pints of yellow paint).
From the first equation:
7/4 = (7+x)/(4+y)
Cross-multiplying gives us:
7(4+y) = 4(7+x)
Simplifying further:
28 + 7y = 28 + 4x
Now let's use the second equation:
7 + 4 = 44
Simplifying:
11 = 44
This is clearly not true, so we made an error in our setup. Let's go back to the first equation and try again.
7/4 = (7+x)/(4+y)
Cross-multiplying gives us:
7(4+y) = 4(7+x)
Expanding gives us:
28 + 7y = 28 + 4x
Subtracting 28 from both sides gives us:
7y = 4x
Now we can use the second equation:
7 + 4 = 44
Simplifying:
11 = 44
Again, this is not true, so we made another mistake. The error lies in the setup of the original problem.
The correct setup should be:
(blue paint)/(yellow paint) = (total blue paint)/(total yellow paint)
7/4 = x/y
To solve for x and y, we need another equation.
We know that the total amount of paint used will be 44 pints:
(blue paint + yellow paint) = total paint
7 + 4 = 44
Simplifying:
11 = 44
This is clearly not true, so we need to re-evaluate our approach.
Since we are given the ratio of blue paint to yellow paint (7:4), we can assume that the additional pints of blue and yellow paint are in the same ratio.
Let's assign variables to the additional pints of blue and yellow paint. Let x be the additional pints of blue paint and y be the additional pints of yellow paint.
Since the ratio of blue paint to yellow paint is 7:4, we can set up the equation:
x/y = 7/4
To find the values of x and y, we also know that the total amount of paint used will be 44 pints. So we can set up another equation:
x + y = 44
Now we have a system of equations:
x/y = 7/4
x + y = 44
To solve this system, we can use substitution. Solve one of the equations for one variable and substitute it into the other equation.
From the equation x/y = 7/4, we can cross-multiply:
4x = 7y
Rearrange the equation to solve for x:
x = (7/4)y
Now substitute this expression for x into the other equation:
(7/4)y + y = 44
Combine like terms:
(11/4)y = 44
Multiply both sides by 4/11 to isolate y:
y = (44 * 4) / 11
Simplify:
y = 16
Now substitute this value back into x = (7/4)y:
x = (7/4) * 16
Simplify:
x = 28
So, with a total of 44 pints, you will have 28 pints of blue paint and 16 pints of yellow paint.