Please explain how to get the answer.
At the animal shelter, 1/3 of the animals are dogs, 2/12 are cats, and 19 are other animals. How many animals are at the shelter?
I said 1/3x + 2/12x + 19 =
4/12x + 2/12x = 19=
6/12x = 19
1/2x = 19
x =
Your first equation is incomplete, but if you make the final step, your answer will be correct.
1/3x + 2/12x + 19 = x OR
19 = x - 1/3x - 2/12x
19 = x - 2/6x - 1/6x
19 = x - 1/2x = 1/2x
38 = x
How does a 4th grader draw a picture to support this answer?
To find the total number of animals at the shelter, you'll need to solve for the variable x in the equation:
1/3x + 2/12x + 19 = x
Step 1: Simplify the fractions on the left side of the equation.
The fraction 2/12 can be reduced to 1/6 by dividing both the numerator and denominator by the greatest common divisor, which is 2.
The equation becomes:
1/3x + 1/6x + 19 = x
Step 2: Combine like terms on the left side of the equation.
The fractions 1/3x and 1/6x have the same denominator of 6x, so they can be added together.
The equation becomes:
2/6x + 1/6x + 19 = x
Simplifying the fractions gives:
3/6x + 19 = x
Step 3: Get rid of the fractions by multiplying both sides of the equation by 6, which is the least common multiple of 6 and x.
6 * (3/6x + 19) = 6 * x
This simplifies to:
3x + 114 = 6x
Step 4: Isolate the variable x by moving all terms containing x to one side of the equation.
Subtract 3x from both sides of the equation:
3x + 114 - 3x = 6x - 3x
This simplifies to:
114 = 3x
Step 5: Solve for x by dividing both sides of the equation by 3.
114 / 3 = 3x / 3
This simplifies to:
38 = x
So, the variable x represents the total number of animals at the shelter, and in this case, it is equal to 38. Therefore, there are 38 animals at the shelter.