what is the equation for One worker makes 3 times as

many widgets as the average
person. A second worker
makes 7/5 times as many
widgets as the average
person. How many times more
widgets does the first worker
make than the second worker?

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

Let's denote the average number of widgets made by a person as \( x \).

According to the problem:

1. The first worker makes \( 3x \) widgets (3 times the average).
2. The second worker makes \( \frac{7}{5} x \) widgets (7/5 times the average).

Now, we want to find how many times more widgets the first worker makes than the second worker. To do this, we can set up the equation:

\[
\text{Ratio} = \frac{\text{Widgets made by first worker}}{\text{Widgets made by second worker}} = \frac{3x}{\frac{7}{5}x}
\]

The \( x \) in the numerator and denominator cancels out:

\[
\text{Ratio} = \frac{3}{\frac{7}{5}} = 3 \times \frac{5}{7} = \frac{15}{7}
\]

Thus, the first worker makes \( \frac{15}{7} \) times as many widgets as the second worker.

To express how many times more widgets the first worker makes than the second worker, we can subtract 1:

\[
\frac{15}{7} - 1 = \frac{15}{7} - \frac{7}{7} = \frac{8}{7}
\]

So, the first worker makes \( \frac{8}{7} \) (or approximately 1.14) times more widgets than the second worker.