If 1 bucket + 5 jars = 1 tub, and 3 buckets + 2 jars = 2 tubs, how many jars are equal to 1 tub?
1t = 1b+5j
3b = 2t-2j
1t = (2t-2j)/3+5j
3t = 2t-2j+15j
1t = 13j
Let's solve this step-by-step:
Given:
1 bucket + 5 jars = 1 tub (Equation 1)
3 buckets + 2 jars = 2 tubs (Equation 2)
To find how many jars are equal to 1 tub, we need to eliminate the buckets from the equations.
Let's multiply Equation 1 by 3 and Equation 2 by 1 to balance the number of buckets:
3 buckets + 15 jars = 3 tubs (Equation 3)
3 buckets + 2 jars = 2 tubs (Equation 4)
Now, we can subtract Equation 4 from Equation 3 to eliminate the buckets:
(3 buckets + 15 jars) - (3 buckets + 2 jars) = 3 tubs - 2 tubs
Simplifying the equation:
(3 - 3) buckets + (15 - 2) jars = 3 - 2 tubs
0 buckets + 13 jars = 1 tub
So, we can conclude that 13 jars are equal to 1 tub.
To find out how many jars are equal to 1 tub, we need to determine the value of 1 jar.
Let's start with the given information:
1 bucket + 5 jars = 1 tub
3 buckets + 2 jars = 2 tubs
Now, let's isolate the number of jars in each equation.
The first equation tells us that 1 tub is equal to 1 bucket + 5 jars.
Rearranging the equation, we can deduce that 5 jars is equal to 1 tub - 1 bucket.
Similarly, the second equation states that 2 tubs are equal to 3 buckets + 2 jars.
Rearranging the equation, we can deduce that 2 jars is equal to 2 tubs - 3 buckets.
Now, we have two equations:
5 jars = 1 tub - 1 bucket
2 jars = 2 tubs - 3 buckets
To find the value of 1 tub, we need to eliminate the buckets from the second equation. Since 1 tub is equivalent to 3 buckets + 2 jars, we can substitute that value into the second equation:
2 jars = 2(3 buckets + 2 jars) - 3 buckets
Simplifying this equation, we have:
2 jars = 6 buckets + 4 jars - 3 buckets
Now, let's combine like terms:
2 jars = (6 buckets - 3 buckets) + 4 jars
Simplifying further:
2 jars = 3 buckets + 4 jars
To isolate the number of jars, we can subtract 3 buckets from both sides of the equation:
2 jars - 3 buckets = 3 buckets + 4 jars - 3 buckets
2 jars - 3 buckets = 4 jars
Now, combining like terms again:
-3 buckets = 2 jars
To continue with our original goal, finding the value of 1 tub, we can substitute the value of -3 buckets into the first equation:
5 jars = 1 tub - 1 bucket
5 jars = 1 tub - (-3 jars)
5 jars = 1 tub + 3 jars
Subtracting 3 jars from both sides of the equation:
5 jars - 3 jars = 1 tub + 3 jars - 3 jars
2 jars = 1 tub
Therefore, 2 jars are equal to 1 tub.