Respuesta :
Answer:
Therefore, the original ratio was 6/12, which can be simplified to 1/2.
Step-by-step explanation:
Here's how to solve this problem:
Let's represent the original fraction:
Numerator: x
Denominator: y
Set up an equation based on the given information:
(x + 7) / (y + 7) = 13/19
Solve for the relationship between x and y:
19(x + 7) = 13(y + 7) (Cross-multiply)
19x + 133 = 13y + 91
19x - 13y = -42
To find possible values of x and y, we can use trial and error while keeping in mind that fractions are usually represented by their simplest form:
Try simple values for x or y. For example, if we start with y = 6:
19x - (13 * 6) = -42
19x = 36
x = 36/19 (This doesn't give us a whole number)
Let's try y = 12:
19x - (13 * 12) = -42
19x = 114
x = 6
We found a solution:
x = 6
y = 12
Therefore, the original ratio was 6/12, which can be simplified to 1/2.
