Six small marbles and four large marbles have a combined weight of 30 g, whilst seven small marbles and two large marbles have a weight of 23 g. Find the weight of a large marble.
Can someone help me create the equation? Thanks.
Just like it says:
6s +4l = 30 ---as is ---> 6s + 4l = 30
7s + 2l = 23 --times 2--> 14s + 4l = 46
subtract them:
8s = 16
s = 2
in the first ----> 12 + 4l = 30
4l = 18
l = 9/2 or 4.5
the large marble weighs 4.5 g, the smaller 2 g
"in the first ----> 12 + 41 = 30"
Sorry if this sounds dumb, but where does the 12 come from?
Sure! To create the equation, let's assign variables to the unknowns. Let's represent the weight of a small marble as 's' and the weight of a large marble as 'L'.
We are given two sets of information:
1) Six small marbles and four large marbles have a combined weight of 30 g
So, the equation for the first set of marbles would be:
6s + 4L = 30 ----(Equation 1)
2) Seven small marbles and two large marbles have a weight of 23 g
So, the equation for the second set of marbles would be:
7s + 2L = 23 ----(Equation 2)
Now we have a system of two equations. By solving this system, we can find the weight of a large marble.
To solve the system, there are several methods you can use, such as substitution or elimination. Let's use the elimination method in this case.
Multiply Equation 2 by 2 so that the coefficients of 'L' in both equations are the same:
14s + 4L = 46
Now, subtract Equation 1 from the modified Equation 2:
14s + 4L - (6s + 4L) = 46 - 30
Simplifying the equation:
14s + 4L - 6s - 4L = 16
8s = 16
s = 2
Now, substitute the value of 's' into either Equation 1 or 2. Let's use Equation 1:
6(2) + 4L = 30
12 + 4L = 30
4L = 30 - 12
4L = 18
L = 18/4
L = 4.5
Therefore, the weight of a large marble is 4.5 g.