The ratio of the number of bathing suits Dina had to the number of bathing suits Yana had was 4:1. After Dina threw out 26 bathing suits, she had 2 fewer than Yana. How many bathing suits did Dina have to begin with?
I was kinda confused at first, but then realized that the answer was d=32
d/y = 4/1
d-26 = y-2
so, to find d, note that y = d/4. So,
d-26 = d/4 - 2
3/4 d = 24
d = 32
y = 8
check:
32/8 = 4/1
32-6 = 26-2
thanks
Well, it seems like Dina really knows how to dive into a pile of bathing suits! Let's solve this problem one splash at a time.
Let's assume that Dina had 4x bathing suits to start with, and Yana had 1x bathing suit. After Dina threw out 26 bathing suits, she had 2 fewer than Yana. So, that means she had 1x - 26 - 2 = 1x - 28 bathing suits left.
Since the ratio of the number of bathing suits Dina had to the number of bathing suits Yana had was 4:1, we can set up the equation:
4x = 1x - 28
Now let's solve for x:
4x - 1x = -28
3x = -28
x = -28/3
Now, since we can't have a negative number of bathing suits, it looks like Dina might have gone a little overboard with throwing away those suits. So unfortunately, it seems that there was no solution to this problem. Looks like Dina needs to go shopping for some new swimsuits!
Let's assign variables to represent the number of bathing suits Dina and Yana had.
Let's say the number of bathing suits Dina had is x and the number of bathing suits Yana had is y.
Given that the ratio of the number of bathing suits Dina had to the number of bathing suits Yana had was 4:1, we can write the equation:
x/y = 4/1
After Dina threw out 26 bathing suits, she had 2 fewer than Yana. So, we can write another equation:
(x - 26) = (y - 2)
Now we have a system of equations:
x/y = 4/1
x - 26 = y - 2
To solve this system of equations, we can use substitution or elimination. Let's use substitution method:
From the first equation, we can isolate x:
x/y = 4/1
x = 4y
Now we can substitute x in the second equation:
4y - 26 = y - 2
Simplifying this equation, we get:
3y = 24
Dividing both sides by 3, we find:
y = 8
Substituting the value of y back into the first equation, we can find x:
x = 4y = 4(8) = 32
Therefore, Dina had 32 bathing suits to begin with.