I have been asked to answer questions in parts in relation to a story problem, but I am having difficulty finding the right formulas. Did I do this right...If not, please help me and tell me where I went wrong.
Part B
The landscaper that maintains Mrs. Jones’ lawn charges a flat fee of $30.00 for each job plus $10.00 per hour for labor.
a. Translate the problem situation into an algebraic equation using C for total cost and h for hours.
30+10h=c
Starting next week, the landscaper is raising his hourly rate to $15.00 per hour but reducing his flat fee to $27.50.
b. Translate the new problem situation into an algebraic equation using C for total cost and h for hours.
27.50+15h=c
c. Mrs. Jones has decided to have the landscaper come for 5 hours per week. How much more money will she be paying each week at these new rates? Use the equations you wrote in parts a and b above to find your answer making sure to show all the work.
First, we figure out the cost of labor and flat rate at the old rate:
30+(10*5)=c
30+50=c
30+50=80.00
Now, we figure out the cost at the new rate:
27.50+ (15*5) =c
27.50+75.00=c
27.50+75.00=102.5
Now we need to find out how much more she will be paying with the new rates…we do this by subtracting:
102.50-80.00=22.50
The end result is that she will be paying 22.50 more for labor with the new rates.
Part C
Mrs. Jones needs to mail a letter to the landscaper. The Post Office charges 37 cents for the first ounce and 23 cents per ounce for each additional ounce. What is the maximum weight of a first-class envelope that can be mailed for no more than $2.50?
a. Write an inequality that models this situation.
.37+ (.23b) <, or equal to 2.50
Solve the inequality showing all steps in the process
First, I I subtract.37 from both sides
.37-.37(.23x) <, or equal to2.50-.37
Now we have .23x<, or equal to 2.13
Now we divide.23 to both sides
.23/.23<, or equal to 2.13/.23
We now have x<, or equal to 9.26lbs
all right, except the last
x<9.26 ounces
Your numbers look fine to me, except for two things.
The letter must weigh nine OUNCES or less not pounds. If it weighed 9.26 ounces, it would be priced by the post office as ten ounces.
I very much appreciate you showing all your work.
The rates of the US Postal Service have changed since that questiuon was written. It is now 44 cents for the first ounce and 17 cents for additional ounces. That has nothing to do with the correctness of your answer, but I thought you might be interested.
Thank you, so much, I always second guess everything I do, and I was unsure whether I did the equation set up right. Other than the mistake of putting it into pounds,rather than ounces all aspects are right even the beginning labor equations?
Thank you so much for your help guys!
Great job breaking down the problem and showing your work! Your approach is correct and you have correctly solved the equations and inequalities.
For Part B, you correctly translated the problem situations into algebraic equations using the variables C for total cost and h for hours. Your equations are:
a. Original situation: C = 30 + 10h
b. New situation: C = 27.50 + 15h
You then used these equations to find the total cost for Mrs. Jones when the landscaper works for 5 hours per week. By substituting h = 5 into the equations, you correctly found:
a. Original cost: C = 30 + 10(5) = $80.00
b. New cost: C = 27.50 + 15(5) = $102.50
To find how much more Mrs. Jones will be paying with the new rates, you subtracted the original cost from the new cost:
$102.50 - $80.00 = $22.50
Therefore, Mrs. Jones will be paying $22.50 more for labor with the new rates.
For Part C, you correctly wrote the inequality that models the situation:
0.37 + 0.23b ≤ 2.50
Then, you performed the steps to solve the inequality properly. By subtracting 0.37 from both sides, you obtained:
0.23b ≤ 2.13
Next, you divided both sides by 0.23:
b ≤ 9.26 lbs
This means that the maximum weight of a first-class envelope that can be mailed for no more than $2.50 is 9.26 lbs.
Overall, your approach and calculations are correct in all the parts. Well done!