If `(9)/(10)y-(7)/(10)y=(4)/(2)-(8)/(15)`, what is the value of y?

Answer

To solve the equation \(\frac{9}{10}y - \frac{7}{10}y = \frac{4}{2} - \frac{8}{15}\), we will follow these steps:

### Step 1: Simplify the Left Side
The left side of the equation is \(\frac{9}{10}y - \frac{7}{10}y\). Since both terms have the same denominator, we can subtract the numerators directly:

\[ \frac{9y - 7y}{10} = \frac{2y}{10} \]

### Step 2: Simplify the Right Side
Now, we simplify the right side of the equation, which is \(\frac{4}{2} - \frac{8}{15}\). First, we simplify \(\frac{4}{2}\):

\[ \frac{4}{2} = 2 \]

Now we need to subtract \(2 - \frac{8}{15}\). To do this, we convert \(2\) into a fraction with a denominator of \(15\):

\[ 2 = \frac{2 \times 15}{1 \times 15} = \frac{30}{15} \]

Now we can perform the subtraction:

\[ \frac{30}{15} - \frac{8}{15} = \frac{30 - 8}{15} = \frac{22}{15} \]

### Step 3: Set the Left Side Equal to the Right Side
Now we have:

\[ \frac{2y}{10} = \frac{22}{15} \]

### Step 4: Cross Multiply
To eliminate the fractions, we can cross multiply:

\[ 2y \cdot 15 = 22 \cdot 10 \]

This simplifies to:

\[ 30y = 220 \]

### Step 5: Solve for \(y\)
Now, we divide both sides by \(30\):

\[ y = \frac{220}{30} \]

### Step 6: Simplify the Fraction
We can simplify \(\frac{220}{30}\) by dividing both the numerator and the denominator by \(10\):

\[ y = \frac{22}{3} \]

Thus, the value of \(y\) is \(\frac{22}{3}\).

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