Ron puts all his nails into 2 large boxes and 6 small boxes. There are 20 more nails in one large box than one small box. The number of nails in the 2 large boxes was 1/2 as many as the number of nails in the 6 small boxes. Find the number of nails in 1 large box.
ASAP plz
g = large , s = small
g = s + 20
2 g = (6 s) / 2
substituting ... 2 (s + 20) = 3 s ... 2 s + 40 = 3 s
find s , then substitute back to find g
To solve this problem, we can start by assigning variables to the unknown quantities. Let's call the number of nails in one large box "x" and the number of nails in one small box "y".
We're told that there are 20 more nails in one large box than one small box. This can be represented as:
x = y + 20 ...(Equation 1)
We're also told that the number of nails in the 2 large boxes is half as many as the number of nails in the 6 small boxes. This can be represented as:
2x = (6y)/2 ...(Equation 2)
Now, let's solve these equations to find the values of x and y.
Since Equation 1 gives us the value of x in terms of y, we can substitute this value of x in Equation 2 to get:
2(y + 20) = (6y)/2
Simplifying the equation, we get:
2y + 40 = 3y
Moving all the terms to one side, we have:
3y - 2y = 40
Simplifying further, we get:
y = 40
Now, we can substitute the value of y back into Equation 1 to find the value of x:
x = y + 20
x = 40 + 20
x = 60
Therefore, there are 60 nails in one large box.