how would you approach this problem..the difference between two numbers is 2184..the larger number is 3 times the smaller number
L=3S
L-S=2184
Are not those math sentences identical to the word sentences?
yes but i don't know how to go about getting the uniknowns or which perspective to use to find it..any ideas it comes from an estimation section in a 4th grade workbook
To approach this problem, follow these steps:
Step 1: Assign variables
Let's assign variables to the larger and smaller numbers. Let L represent the larger number, and S represent the smaller number.
Step 2: Set up equations
Based on the given information, we know that the difference between two numbers is 2184, and the larger number is 3 times the smaller number. We can set up the following equations:
L - S = 2184 (Equation 1)
L = 3S (Equation 2)
Step 3: Solve the system of equations
There are multiple ways to solve this system of equations. In this case, we will use substitution.
Substitute Equation 2 into Equation 1:
3S - S = 2184
2S = 2184
S = 2184 / 2
S = 1092
Step 4: Find the larger number
Substitute the value of S into Equation 2:
L = 3 * 1092
L = 3276
Therefore, the larger number is 3276 and the smaller number is 1092.
To approach this problem, you can set up a system of equations using the given information. Let's call the larger number "L" and the smaller number "S".
From the problem statement, we know two things:
1) The difference between the two numbers is 2184: L - S = 2184
2) The larger number is 3 times the smaller number: L = 3S
To solve this system of equations, we can use the method of substitution or elimination.
Method 1: Substitution
1) Rewrite one of the equations to solve for one variable in terms of the other:
L = 3S
2) Substitute this expression for L into the other equation:
(3S) - S = 2184
3) Simplify and solve for S:
2S = 2184
S = 1092
4) Substitute the value of S back into one of the equations to find L:
L = 3(1092)
L = 3276
So, the smaller number is 1092 and the larger number is 3276.
Method 2: Elimination
1) Multiply the second equation by -1 to make both equations have the same coefficient for L:
-L = -3S
2) Add the two equations together to eliminate L:
(L - S) + (-L) = 2184 + (-3S)
-S = 2184 - 3S
3) Simplify and solve for S:
2S = -2184
S = -1092
4) Substitute the value of S back into one of the equations to find L:
L = 3(-1092)
L = -3276
However, in the given problem, we are dealing with numbers, so it's not reasonable to have a negative value as the solution. Thus, we can conclude that an error has occurred, either in the formulation of the problem or the given values.
In summary, the problem encountered an error as it led to a negative solution, which is not possible for a real-world scenario.