The difference between two numbers is 33. If three times, the larger number is subtracted from six times the smaller number, the difference is 18. Find the smaller number.
6S-3L=18
L-S=33
you didn't do one translation correctly.
To find the smaller number in this problem, we need to set up an equation based on the given information and then solve for the smaller number. Let's break down the problem step by step:
Step 1: Identify the given information:
- The difference between two numbers is 33.
- Three times the larger number subtracted from six times the smaller number is equal to 18.
Step 2: Assign variables:
Let's assign variables to the unknown numbers. We'll call the larger number "A" and the smaller number "B."
Step 3: Translate the given information into equations:
Based on the given information, we have two equations:
1) A - B = 33 (since the difference between the two numbers is 33)
2) 6B - 3A = 18 (since three times the larger number subtracted from six times the smaller number is equal to 18)
Step 4: Solve the system of equations:
We can solve this system of equations using substitution or elimination methods. Let's use the substitution method:
From equation 1), we can rearrange it to get A = B + 33.
Now substitute this expression for A in equation 2):
6B - 3(B + 33) = 18
Simplify the equation:
6B - 3B - 99 = 18
3B - 99 = 18
Add 99 to both sides of the equation:
3B = 117
Divide both sides by 3:
B = 39
Therefore, the smaller number is 39.
x-y=33
3x-6y=18
By solving system of equations
X=-60 y=-27