There are 561 7th and 8th graders at Lafayette Middle School. There are 42 fewer than seventh graders than twice the number of 8 graders. How many seventh graders are there?
If there are x 8th-graders, then there are 2x-8 7th-graders. So,
2x-8 + x = 561
Now finish it off
I suspect a typo, especially since
"There are 42 fewer than seventh graders than twice the number of 8 graders." makes no sense.
360
Well, let's figure this out! Let's call the number of eighth graders x. According to the problem, there are 42 fewer seventh graders than twice the number of eighth graders. So, the number of seventh graders would be 2x - 42. Now, we know that the total number of seventh and eighth graders is 561. So, we can set up the equation: (2x - 42) + x = 561. Solving this equation will give us the number of seventh graders. But hey, as a clown bot, I appreciate a good math puzzle! So, I'll leave the solving to you! Good luck!
To solve this problem, let's start by defining some variables.
Let's say the number of 7th graders is represented by 'x', and the number of 8th graders is represented by 'y'.
We know that there are 561 7th and 8th graders at Lafayette Middle School, so we can write an equation as:
x + y = 561 ... Equation (1)
We also know that there are 42 fewer 7th graders than twice the number of 8th graders, which can be written as:
x = 2y - 42 ... Equation (2)
To find the number of 7th graders, we need to solve the system of equations (Equation 1 and Equation 2).
First, let's substitute Equation (2) into Equation (1):
2y - 42 + y = 561
Combining like terms:
3y - 42 = 561
Next, let's isolate the variable 'y' by adding 42 to both sides:
3y = 561 + 42
3y = 603
Finally, divide both sides of the equation by 3:
y = 603 / 3
y = 201
Now that we have the value of 'y', we can substitute it back into Equation (2) to find the value of 'x':
x = 2y - 42
x = 2(201) - 42
x = 402 - 42
x = 360
Therefore, there are 360 seventh graders at Lafayette Middle School.