J and I collect yo-yos.The ratio to Js yo-yos to Is is 5:4. If J loses 15 of her yo-yos then she and I will have the same number of yo-yos in their collection. How many yo-yos do both have together?
Let's say the number of yo-yos J has is 5x.
The number of yo-yos I have is 4x.
If J loses 15 yo-yos, the total number of yo-yos J and I will have is (5x-15)+(4x)= 9x-15=4x
Combining like terms, we get 5x=15
The value of x is 15/5 = <<15/5=3>>3
The total number of yo-yos that both have is (5x+4x) =5*3+4*3 = 15+12 = <<5*3+4*3=27>>27. Answer: \boxed{27}.
To solve this problem, we need to set up an equation based on the given information.
Let's assume that J has x yo-yos and I has y yo-yos.
According to the ratio given, the number of J's yo-yos to I's yo-yos is 5:4. This can be expressed as x/y = 5/4.
Next, we know that if J loses 15 yo-yos, she will have x - 15 yo-yos, and she and I will have the same number of yo-yos. So, we can set up another equation: x - 15 = y.
Now we have a system of equations:
x/y = 5/4 (equation 1)
x - 15 = y (equation 2)
To solve this system of equations, we can use the substitution method.
From equation 2, we can express x in terms of y: x = y + 15.
Substituting this value of x into equation 1, we have: (y + 15)/y = 5/4.
Cross-multiplying, we get: 4(y + 15) = 5y.
Expanding the equation, we have: 4y + 60 = 5y.
Subtracting 4y from both sides, we have: 60 = y.
So, I has 60 yo-yos.
To find the number of yo-yos J has, we can substitute this value of y into equation 2: x - 15 = 60.
Adding 15 to both sides, we have: x = 75.
Therefore, J has 75 yo-yos.
Finally, to find the total number of yo-yos both have together, we can add J's and I's yo-yos: 75 + 60 = 135.
So, both J and I have a total of 135 yo-yos together.
Let's say J initially has 5x yo-yos, and I has 4x yo-yos.
If J loses 15 yo-yos, then she will have 5x - 15 yo-yos.
At this point, J and I will have the same number of yo-yos, so we can set up an equation:
5x - 15 = 4x
By solving this equation, we can determine the value of x:
5x - 4x = 15
x = 15
Therefore, both J and I would have:
J: 5x = 5 * 15 = 75 yo-yos
I: 4x = 4 * 15 = 60 yo-yos
Together, J and I would have: 75 + 60 = 135 yo-yos
So, both J and I would have a total of 135 yo-yos together.