One-third of a number increased by 8 is 37

Answer 1

So in this case, you would have to know how to translate the word problem into equation form.

The word "of" implies multiplication. For example, if you say "the product of 2 and 4 is 8", what you are really saying is " 2 multiplied by 4 is 8", and in equation form that is 2 X 4 = 8

So to answer this question, the term "one-third" is as simple way of saying the fraction 1/3. So what you are really saying is (1/3)x + 8 = 37. I've spelled this out below.

One-third = (1/3)

of a number = x

increased = +

by 8 = 8

is 37 = 37

Now that we have our equation, lets find what x is by isolating it. First we add like terms, in this case it's the positive 8 and the 37. The easiest method would be to move the 8 to the other side of the equals sign, but in order to do this, we have to change it's sign. So now we have

(1/3)x = 37-8

This goes to

(1/3)x = 29

Now that we have this, we need to isolate the x variable still. It is currently being multiplied by (1/3), so we have to do the opposite of multiplication on both sides of the equation in order to isolate it. The opposite of multiplication is division. At this point we divide both sides by 1/3.

When we divide the left side by 1/3, it cancels out and leaves x, however when we divide the right side by 1/3 we get

29 / (1/3)

The slash sign above implies division. We are dividing by a fraction, and the rule for dividing fractions is that you flip the second fraction, and simply multiply top by the top and bottom by the bottom. We turn 29 into a fraction in order to do this, and 29 as a fraction is simply (29/1). So now we have

(29/1) X (3/1)

Notice that the 1/3 is now flipped to 3/1. Remember that we flip it due to the rule mentioned above. So we multiply the numerators together and the denominators together. The numerators are 29 and 3, and the denominators are each 1. 29 multiplied by 3 is 87, and 1 multiplied by 1 is simply 1. So our answer is 87/1, which is simply 87.

The final answer is x=87

Answer 2

x/3+8=37

x/3=29

x=97