duwayne wrote a two-digit number. he multiplied it by 3, added 18, and divided by 8. his final answer was 9. what number did duwayne write?
Go backwards and do the opposite. (9x8)=x
x-18=y
y/3 = z
2-digit no --- x
multiplied by 3 --- 3x
added 18 --- 3x+18
divided by 8 --- (3x+18)/8
got 9
(3x+18)/8 = 9
3x+18 = 72
3x = 54
x =18
thank you. how did you get raid of the 8 on the left side?
3x+4y=18;kx_4y=180 solved?
To find the two-digit number that Duwayne wrote, we can work backward through the calculations that were done.
Let's start with the final answer of 9 and work our way back to find the original number.
1. Duwayne started with a number.
2. He multiplied it by 3.
3. He added 18 to the result.
4. He divided the sum by 8.
5. The final answer was 9.
So we can set up an equation to represent the steps:
(x * 3 + 18) / 8 = 9
Now, let's solve for x to find the original number Duwayne wrote.
To eliminate the denominator, we can multiply both sides of the equation by 8:
8 * (x * 3 + 18) / 8 = 9 * 8
This simplifies to:
x * 3 + 18 = 72
Next, let's isolate the variable x by subtracting 18 from both sides:
x * 3 = 72 - 18
This simplifies to:
x * 3 = 54
Now, divide both sides of the equation by 3 to solve for x:
x = 54 / 3
This simplifies to:
x = 18
Therefore, the two-digit number that Duwayne wrote is 18.