Answer :

We start with the equation

[tex]$$
\frac{14}{15} = \frac{x+9}{60}.
$$[/tex]

Step 1. Cross Multiply

Multiply both sides by [tex]$15 \times 60$[/tex] to eliminate the fractions:

[tex]$$
14 \times 60 = 15 \times (x+9).
$$[/tex]

Step 2. Compute the Multiplications

Calculate the left-hand side:

[tex]$$
14 \times 60 = 840.
$$[/tex]

Next, expand the right-hand side:

[tex]$$
15 \times (x+9) = 15x + 15 \times 9 = 15x + 135.
$$[/tex]

So, the equation becomes:

[tex]$$
840 = 15x + 135.
$$[/tex]

Step 3. Isolate the Term with [tex]$x$[/tex]

Subtract [tex]$135$[/tex] from both sides to isolate the term with [tex]$x$[/tex]:

[tex]$$
840 - 135 = 15x.
$$[/tex]

Compute the subtraction:

[tex]$$
840 - 135 = 705.
$$[/tex]

Now, the equation is:

[tex]$$
705 = 15x.
$$[/tex]

Step 4. Solve for [tex]$x$[/tex]

Divide both sides by [tex]$15$[/tex] to solve for [tex]$x$[/tex]:

[tex]$$
x = \frac{705}{15}.
$$[/tex]

Perform the division:

[tex]$$
\frac{705}{15} = 47.
$$[/tex]

Final Answer

[tex]$$
x = 47.
$$[/tex]

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