So it seems as if the first problem is asking this:
.
If x=0.15, then 11/15*(0.15) is 0.11 or 11/100.
The second problem is asking:
To solve algebraically, you want to get rid of the denominators under the x's. To do so, you want to multiply by the Least Common Multiple (LCM) of the denominators. For 3 and 4, the LCM is 12. Multiply everything by 12 to get:
Problem 1 We are to solve <span>2 1/6 - 11/15 x = 0.15 for x. Step 1: Identify the LCD. Taking the product of 6 and 15, we get the LCD 90.
Then 2 1/6 becomes 13/6, or 195/90, and - (11/15)x becomes -(66x/90). We must also convert 0.15 to an improper fraction with denominator 90:
0.15(90)/90 = 13.5/90
Combine these two same-LCD fractions: 195/90 - 77x
and equate this result, 195/90 - (66x)/90 = 13.5/90.
We can now eliminate the denominator, 90, from all three terms:
195 - 66x = 13.5
Let's elim. the decimal fraction; to do this, mult all three terms by 2:
390 - 132x = 27
Then 390-27= 132x => 363 = 132x
Dividing both sides by 132, x = 363/132 (This can be reduced to
x = 11/4, or x = 2.75.
We must check this result. Does 2 1/6 - (11/15)(2.75) = 0.15?
Does 13/6 - 121/60 = 0.15?
Does 130/60 - 121/60 = 0.15?
Does 9/60 = 0.15? YES. So the solution here is x = 2.75 or x= 11/4.
Next time, please post only ONE question at a time. But for now, I will address your
Problem #2:
Solve for x: </span><span>x/4 + 1/2 = x/3 + 1/6 1. The LCD is 12. Note that 12 is evenly divisible by 4, 2, 3 and 6. 2. Multiplying all four terms by 12 allows us to write the equation as
12(x/4) + 12(1/2) = 12(x/3) + 12/6
Simplifying, 3x + 6 = 4x + 2, which results in x = 4.
Check: If we subst. x =4, is </span><span>x/4 + 1/2 = x/3 + 1/6 true?
Is this true? 4/4 + 1/2 = 4/3 + 1/6
Is 1 + 1/2 = 4/3 + 1/6? Is 1 1/2 = 8/6 + 1/6?
Is 3/2 = 9/6? Is 3/2 = 3/2? YES. So here, x =4 is a solution.
Well the way I see it is he started with 4 villager so I would see the equation to be
1.13x times 17+4 would equal the amount of villagers he could have which would be 23.21 as for the equation it would be 1.13x times 17 plus four equals the number of villagers total