Orange and white ping-pong balls are sold in either Package $A$ or Package $B$. Each package contains the same number of ping-pong balls.
The ratio between the numbers of white and orange ping-pong balls in Package $A$ is $2:3.$
The ratio between the numbers of white and orange ping-pong balls in Package $B$ is $3:4.$
The ratio between the numbers of Package $A$ and Package $B$ in the store is $4:5.$
What is the ratio between the numbers of white and orange ping-pong balls in all these packages combined? Write your answer in the form of a fraction.
You can not use x for all of them. You have to change the variable. As for Bob , please do not put your homework questions in the internet. No searching up the answers.
I agree with someone but what's the answer
Let's start by assigning variables to the unknown quantities in the problem.
Let the number of white ping-pong balls in Package $A$ be $2x$, and the number of orange ping-pong balls in Package $A$ be $3x$. This means that there are $2x$ white ping-pong balls and $3x$ orange ping-pong balls in Package $A$.
Similarly, let the number of white ping-pong balls in Package $B$ be $3y$, and the number of orange ping-pong balls in Package $B$ be $4y$. This means that there are $3y$ white ping-pong balls and $4y$ orange ping-pong balls in Package $B$.
Now, we are given that the ratio between the numbers of Package $A$ and Package $B$ in the store is $4:5$. This means that the number of Package $A$ is $4k$ and the number of Package $B$ is $5k$ for some positive integer $k$.
In total, the number of white ping-pong balls in all packages combined is $2x + 3y$. And the number of orange ping-pong balls in all packages combined is $3x + 4y$.
Since the number of Package $A$ is $4k$ and the number of white ping-pong balls in Package $A$ is $2x$, we can set up the equation $2x = 4k$ and solve for $x$. Dividing both sides by $2$ gives us $x = 2k$.
Similarly, since the number of Package $B$ is $5k$ and the number of white ping-pong balls in Package $B$ is $3y$, we can set up the equation $3y = 5k$ and solve for $y$. Dividing both sides by $3$ gives us $y = \frac{5}{3}k$.
Now we can substitute the values of $x$ and $y$ into the expressions for the total number of white and orange ping-pong balls.
The total number of white ping-pong balls in all packages combined is $2x + 3y = 2(2k) + 3\left(\frac{5}{3}k\right) = 4k + 5k = 9k$.
The total number of orange ping-pong balls in all packages combined is $3x + 4y = 3(2k) + 4\left(\frac{5}{3}k\right) = 6k + \frac{20}{3}k = \frac{38}{3}k$.
Therefore, the ratio between the numbers of white and orange ping-pong balls in all these packages combined is $\frac{9k}{\frac{38}{3}k}$. Simplifying this fraction gives $\frac{27}{38}$.
why all the stupid $ signs?
A:B = 4:5
If there are 4x packages of A and 5x packages of B, then there are
So, in all, there are
2*4x + 3*5x white balls
3*4x + 4*5x orange balls
So white : orange = 23/32