Question

Create a proportion using the form = to represent the following word problem.

Answer 1

Answer :
x = 53.85

Step by step explanation:
If 78% of x (some numbers) is equal to 42, then we must set this as an equation to find it.

1) Rewriting 78% as a fraction and considering that when we say 78% of some number (x) we mean a product.
78% = 78/100 ➡️ 78/100x = 42

2) Then we can go on :
100 * 78/100x = 42 * 100
78x = 4200
78x/78 = 4200/78 ➡️ x = 53.85

3) Alternatively, simply dividing 42 by 0.78 (78%) would come to the same result :

42/0.78 = 53.85

Answer 2

To get the solution, we are looking for, we need to point out what we know.

1. We assume, that the number 42 is 100% - because it's the output value of the task.
2. We assume, that x is the value we are looking for.
3. If 42 is 100%, so we can write it down as 42=100%.
4. We know, that x is 78% of the output value, so we can write it down as x=78%.
5. Now we have two simple equations:
1) 42=100%
2) x=78%
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
42/x=100%/78%
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for what is 78% of 42

42/x=100/78
(42/x)*x=(100/78)*x - we multiply both sides of the equation by x
42=1.28205128205*x - we divide both sides of the equation by (1.28205128205) to get x
42/1.28205128205=x
32.76=x
x=32.76