write an expression that models the sum of your earnings for three weeks and Rich's earnings for two weeks if you each work (r) hours per week and Rich receives $15 in tips per week. Simplify the expression.
Assuming the rate (dollars/hr) is the same,
tips for 2 wks + Rich earnings + my earnings.
(2wksx15/wk) + (r hrs/wk x 2wks) + (r hrs/wk x 3 wks) =
30 + 2r + 3r = 30 + 5r
Check my thinking.
Let's break down the problem step-by-step:
1. Let's start by calculating your earnings for three weeks. Since you work (r) hours per week, your total earnings would be the product of your hourly rate and the total number of hours worked. Assuming you earn $x per hour, your earnings for three weeks would be: 3r * x.
2. Now let's calculate Rich's earnings for two weeks. We know that Rich receives $15 in tips per week, so his total earnings from tips for two weeks would be: 2 * $15 = $30.
3. Finally, let's sum up your earnings and Rich's earnings. The expression that models the sum of your earnings for three weeks and Rich's earnings for two weeks would be: 3rx + $30.
Simplifying the expression is not possible unless we have specific values for x and r. The expression can be rewritten as: 3rx + 30.
To model the sum of your earnings for three weeks and Rich's earnings for two weeks, we need to consider your earnings and Rich's earnings separately and then add them together.
Let's start with your earnings. Since you work r hours per week, your earnings per week can be calculated using the formula: Earnings = r * Pay rate. However, the problem doesn't specify your pay rate, so let's denote it as p. Therefore, your earnings for three weeks can be expressed as 3 * (r * p) or simply 3rp.
Next, let's calculate Rich's earnings. It is mentioned that Rich receives $15 in tips per week. Therefore, his earnings per week can be given as: Earnings = (r * Pay rate) + Tips. We already accounted for his tips, so his earnings for two weeks can be written as 2 * (r * p) or 2rp.
Finally, to find the sum of your earnings for three weeks and Rich's earnings for two weeks, we can add the two expressions together:
Total earnings = Your earnings + Rich's earnings
= 3rp + 2rp
= 5rp
Therefore, the expression that models the sum of your earnings for three weeks and Rich's earnings for two weeks is 5rp.