I need help with a word problem. Stella's sock drawer contains 30 pairs of socks. There are 3 times less 2 the number of pink socks than blue socks. How many pairs of pink socks and blue socks does Stella have?
2-3x + x = 30, 2+2-3x + x = 30 +2,
4x/4 = 32/4, x=8, 8 blue & 22 pink. Did I set this up correctly and is answer correct?
the answer is correct, but your equation is wrong
3x-2 + x = 30
4x = 32
Take a look at your arithmetic. The equations don't add up.
so it should be 3x-2 + x = 30
3x-2+2+x = 30+2
3x+x = 32
4x = 32
4x/4 = 32/4
x=8
so it should be 3x-2 + x = 30
3x-2+2+x = 30+2
3x+x = 32
4x = 32
4x/4 = 32/4
x=8
Let's break down the word problem and check your setup.
First, let's assign variables to the unknowns. Let's say "x" represents the number of pairs of blue socks and "y" represents the number of pairs of pink socks.
According to the problem, there are 3 times less 2 the number of pink socks than blue socks. This means that the number of pink socks is 3 times lower than the number of blue socks, minus 2. Mathematically, we can express this as:
y = 3(x - 2)
Next, we are given that Stella's sock drawer contains 30 pairs of socks. This means that the total number of all the pairs of socks (both blue and pink) should be equal to 30:
x + y = 30
Now, let's substitute the value of y from the first equation into the second equation:
x + 3(x - 2) = 30
x + 3x - 6 = 30
4x - 6 = 30
To solve for x, we'll add 6 to both sides of the equation:
4x = 36
Now, dividing both sides of the equation by 4, we get:
x = 9
So, you made a mistake in your setup. It is not 2-3x + x = 30, but rather 4x - 6 = 30.
Now, substituting the value of x back into the equation y = 3(x - 2), we have:
y = 3(9 - 2) = 3(7) = 21
Therefore, the correct answer is 9 pairs of blue socks and 21 pairs of pink socks.