Question

2 2/3:(y+1/3)=1 1/2:(y-1 1/8)

Answer 1

$2 \frac{2}{3} :(y+ \frac{1}{3} )=1 \frac{1}{2} :(y-1 \frac{1}{8} ) \\ 2 \frac{2}{3} *(y-1 \frac{1}{8} )=1 \frac{1}{2} *(y+ \frac{1}{3} ) \\ \frac{8}{3} *(y- \frac{9}{8} )= \frac{3}{2} *(y+ \frac{1}{3} ) \\ \frac{8}{3} y-3= \frac{3}{2} y+ \frac{1}{2} \\ \frac{8}{3} y- \frac{3}{2}y= \frac{1}{2} +3 \\ \frac{7}{6} y=3 \frac{1}{2} \\ y=3 \frac{1}{2} : \frac{7}{6} \\ y= \frac{7}{2} * \frac{6}{7} \\ y=3$

Answer 2

To solve the equation 2 2/3:(y+1/3) = 1 1/2:(y-1 1/8), you can follow these steps:

Step 1: Convert the mixed numbers to improper fractions. 2 2/3 can be written as (3 * 2 + 2)/3 = 8/3 1 1/2 can be written as (2 * 1 + 1)/2 = 3/2 1 1/8 can be written as (8 * 1 + 1)/8 = 9/8

Now, the equation becomes: (8/3) / (y + 1/3) = (3/2) / (y - 9/8)

Step 2: Cross-multiply to eliminate the fractions. (8/3) * (y - 9/8) = (3/2) * (y + 1/3)

Step 3: Solve for y. Let's expand both sides of the equation:

(8/3) * y - (8/3) * (9/8) = (3/2) * y + (3/2) * (1/3)

Now, simplify each side:

(8/3) * y - 3 = (3/2) * y + 1/2

Next, move all terms involving y to one side and constants to the other side:

(8/3) * y - (3/2) * y = 1/2 + 3

Now, find a common denominator for the fractions on the left side:

[(16/6) * y - (9/6) * y] = 7/2

Combine like terms:

(7/6) * y = 7/2

Now, isolate y by multiplying both sides by the reciprocal of (7/6), which is (6/7):

y = (7/2) * (6/7)

y = (7 * 6) / (2 * 7)

y = 42/14

Now, simplify the fraction:

y = 3

So, the solution to the equation is y = 3.