Clara earns an hourly rate of $20 per hour and 5% commission. Rose earns an hourly rate of

$16 per hour and 10% commission. They each work a 40-hour week. In one particular week,
Clara and Rose both sold the same value of goods and both received the same wage. How much
did they sell and what was their wage?

(20 * 40) + .05 s = (16 * 40) + .10 s

solve for s (amount of sales) , then substitute back to find total wage

To find out how much Clara and Rose sold, we need to set up an equation. Let's assume they sold x dollars worth of goods.

For Clara, her wage would be the sum of her hourly pay and her commission:
Wage_Clara = (Hourly_rate_Clara * Hours_worked) + (Commission_rate_Clara * Sold_goods)
Wage_Clara = (20 * 40) + (0.05 * x)
Wage_Clara = 800 + 0.05x

For Rose, her wage would be:
Wage_Rose = (Hourly_rate_Rose * Hours_worked) + (Commission_rate_Rose * Sold_goods)
Wage_Rose = (16 * 40) + (0.10 * x)
Wage_Rose = 640 + 0.10x

Since both Clara and Rose received the same wage, we can set these two equations equal to each other:
800 + 0.05x = 640 + 0.10x

Now we can solve for x, which represents the value of goods sold:
0.05x - 0.10x = 640 - 800
-0.05x = -160
x = (-160)/(-0.05)
x = 3200

Therefore, both Clara and Rose sold goods worth $3200 in that particular week.

To find out their wage, we can substitute the value of x into either of the equations:
Wage_Clara = 800 + 0.05(3200)
Wage_Clara = 800 + 160
Wage_Clara = $960

Wage_Rose = 640 + 0.10(3200)
Wage_Rose = 640 + 320
Wage_Rose = $960

So, both Clara and Rose sold goods worth $3200 and received a wage of $960 in that week.