Tutors Answer Your Questions about Linear Equations And Systems Word Problems (FREE)
Question 521071: Plant A is initially 10 inches tall and it grows 2 inches per week. Plant B is 20 inches tall and grows 1 inch per week. In how many weeks are the plants the same height? I need the systems and I'm having trouble getting them.
Click here to see answer by scott8148(6628)   |
Question 521156: 1.Jason invested $20,000 in two accounts, one paying 7% and the other payijng 9%in annual interest. If the total interest he earned for the year was $1550, how much did he invest in each?
2. Meg owes $13,250 on two student loans. One loan has an APR of 5%; the other, an APR of 8%. If the total interest after one year is $727, what is the amount of each loan?
3.Sharon an Rae are riding bicycles on the same trail in the same directions. Sharon crosses a bridge at 12:18 p.m. Rae crosses the same bridge at 12:33 p.m. If Sharon is going 8 miles per hour and Rae is going 10 miles per hour,when will Rae catch up with Sharon?
4.A pharmicist is preparing a 300-milliliter solution of alcohol. If she has 15% and 45% alcohol solutions in stock, how muchof each must she use?
Click here to see answer by solver91311(16877)  |
Question 521237: In comparing two local well-known DJs for this year’s street dance, you see two good choices. DJ Joe charges $100 for each hour of play time. DJ Dan charges a fee of $150, plus $75 an hour of play time.
a. For two hours of play time, what would be the charge for each and who would charge the lesser amount?
b. For eight hours of play time, what would be the charge for each and who would charge the lesser amount?
c. For how many hours would DJ Joe provide the better deal? Express your answer as an inequality. Explain how you found your answer.
Click here to see answer by mananth(12270)  |
Question 521515: you belong to a school organization that is trying to raise money for its annual trip to new york city. the organization decides to hold a concert at a local site that can accomadate 1500 people. it will cost the organization $1200 to rent the hall and provide security. the band wants $3000 but you get them to agree to a price of $2000 plus 20% of the cost of each ticket sold with a limit of $5000. you are pretty sure the band will attract at least 800 people. if you want the breakeven point to be 800 tickets sold what must be the price of the ticket?
Click here to see answer by josmiceli(9671)  |
Question 522519: A local hospital is holding a two day marathon walk to raise funds for a new research facility. The total distance of the marathon is 26.2 miles. On the first day, Martha starts walking at 10:00 am. She walks 4 miles per hour. Carol starts two hours later than Martha but decides to run to catch up to Martha. Carol runs at a speed of 6 miles per hour. Carol wants to reduce the time she takes to catch up to Martha by 1 hour. How can she do this by changing her starting time? How can she do this by changing her speed?
Click here to see answer by mananth(12270) |
Question 522560: A state emplotees' pension fund invested a total of one million dollars in tow accounts that earned 3.5% and 4.5% annual interest. At the end of the year, the total interest earned form the two investments was $39,000. How much was invested at each rate?
( i cant figure out the 2 equations)
Click here to see answer by Earlsdon(6287) |
Question 522670: Doreen and Irena plan to leave their houses at the same time, roller blade towards each other, and meet fo rlunch after 4 hours on the road. Doreen can maintain a speed of 7 mph, which is 70% of Irena's speed. If they meet exactly as planned, what is the distance between their houses.
Click here to see answer by ankor@dixie-net.com(15649)  |
Question 523692: A model iin new orleans charges $90.00 dollars a day for a double occupacy, and they charge $80.00 for a single occupacy. If 80 rooms are occupied for a total of 6930, how many rooms of eachkind are occupied?
Click here to see answer by Maths68(1474)  |
Question 523684: Polynomials
Retail companies must keep close track of their operations to maintain profitability. Often, the sales data of each individual product is analyzed separately, which can be used to help set pricing and other sales strategies.
1. In this problem, we analyze the profit found for sales of decorative tiles. A demand equation (sometimes called a demand curve) shows how much money people would pay for a product depending on how much of that product is available on the open market. Often, the demand equation is found empirically (through experiment, or market research).
2. Use Equation Editor to write mathematical expressions and equations, where needed
1a.
Suppose a market research company finds that at a price of p = $50, they would sell x = 60 tiles each month. If they lower the price to p = $45, then more people would purchase the tile, and they can expect to sell x = 75 tiles in a month’s time.
1a.
Find the equation of the line for the demand equation. Write your answer in the form:
P = mx + b.
Hint: Find the slope of the line, and then use the Point-Slope formula to solve for the demand. Let x represent Price and y represent Tiles Sold.
Step 1: Write the coordinates for the points on the line
P1 = (50, 60) P2 = (45, 75)
x1, y1 x2, y2
Step 2: Find the slope, using the Slope Equation:
Step 3: Use the Point-Slope Formula to find the equation
y – y2 = m(x – x2)
y – 75 = -3(x - 45) Substitute your values
y – 75 = -3x + 135 Simplify
y = -3x + 210 Solve for y
Final Answer:
P = –3x + 210
STOP! Do not continue until you have sent me the answer to question 1a. Send me your equation in your Individual Folder before continuing. The reason for this is because the rest of this assignment is dependent on getting this equation correct. I will send you the correct equation so that you have a chance of getting the rest of this assignment correct.
A company’s revenue is the amount of money that comes in from sales, before business costs are subtracted. For a single product, you can find the revenue by multiplying the quantity of the product sold, x, by the demand equation, p.
1b.
Substitute the result you found from part a. into the equation R = xp to find the revenue equation. Provide your answer in simplified form.
1b.
The costs of doing business for a company can be found by adding fixed costs, such as rent, insurance, and wages, and variable costs, which are the costs to purchase the product you are selling. The portion of the company’s fixed costs allotted to this product is $1440, and the supplier’s cost for a set of tile is $6.00 each. Let x represent the number of tile sets.
1c
Write the equation for the Cost of Doing Business in the form C = mx + b
1c.
1d.
The profit made from the sale of tiles is found by subtracting the costs from the revenue.
Find the Profit Equation by substituting your equations for R and C in the equation . Simplify the equation.
1d.
1e.
What is the profit made from selling 20 tile sets per month?
1e.
1f.
What is the profit made from selling 25 tile sets each month?
1f.
1g.
What is the profit made from selling no tile sets each month? Interpret your answer.
1g.
1h.
Use trial and error to find the quantity of tile sets per month that yields the highest profit.
1h.
1i.
How much profit would you earn from the number you found in part h?
1i.
1j.
What price would you sell the tile sets at to realize this profit?
1j. Hint: Use the demand equation from part a. and substitute your “x” from 1h.
2.
The break even values for a profit model are the values for which you earn $0 in profit. Use the equation you created in question 1 to solve P = 0, and find your break even values.
2. Hint: Set P= 0 and factor the equation.
3a.
In 2002, Home Depot’s sales amounted to $58,250,000,000. In 2006, its sales were $90,750,000,000.
Write Home Depot’s 2002 sales and 2006 sales in scientific notation.
3a
3b.
You can find the percent of growth in Home Depot’s sales from 2002 to 2006 by following these steps:
- Find the increase in sales from 2002 to 2006.
- Find what percent that increase is of the 2002 sales.
The Home Depot, Inc. (2007, March 29). 2006 Annual Report. Retrieved from http://www6.homedepot.com/annualreport/index.html
3b.
What was the percent growth in Home Depot’s sales from 2002 to 2006? Do all your work by using scientific notation.
4.
A customer wants to make a teepee in his backyard for his children. He plans to use lengths of PVC plumbing pipe for the supports on the teepee, and he wants the teepee to be 16 feet across and 9 feet tall (see figure).
Find the length of the side supports.
4. Hint: Use the Pythagorean Theorem.
End of Application Assignment
Click here to see answer by richard1234(5390)  |
Question 523626: Formulate a system of equations for the situation below and solve.
A theater has a seating capacity of 732 and charges $4 for children, $6 for students, and $8 for adults. At a certain screening with full attendance, there were half as many adults as children and students combined. The receipts totaled $4540. How many children attended the show?
Click here to see answer by ankor@dixie-net.com(15649) |
Question 524141: The weight of a body above sea level varies inversely with the square of the distance from the center of Earth. If a women weighs 119 pounds when she is at sea level, 3960 miles from the center of Earth, how much will she weigh when she is at the top of a mountain, 1.8 miles above sea level?
Click here to see answer by stanbon(57307) |
Question 524388: Describe how to solve a linear equation using the equality properties. Demonstrate the process with an example. Next, replace the equal sign in your example with an inequality by using the less than or greater than sign. Then solve the inequality.
Click here to see answer by solver91311(16877) |
Question 524618: A gardener has up to 270 square feet available for planting flowers and vegetables. The gardener wants thespace used for vegetables to be at least twice the space used for flowers. In addition, at 35 least square feet is to
be used for flowers. Let x denote the area in square feet used for flowers, and y let denote the area in square feet used for vegetables. Shade the region of the plane that represents all allocations of space satisfying these
Click here to see answer by stanbon(57307) |
Question 524740: Hi anyone, Could you help me solve this problem...I keep getting an answer that does not make any sense to me...its the pennies that are confusing..I know they represent p=1 and d=10 but I am having trouble setting up the problem..please help!!!
Chris
Here is the problem: Josh has a change jar that contains only dimes and pennies. He has 32 coins which add up to a total of $1.85. How many of each type of coin does he have?
Click here to see answer by mananth(12270) |
Question 524827: Gavin Royse needs a layout of his yard. He is doing some landscaping and needs to have a grid of his yard for the landscape workers to use when putting in his fence and the two new trees that he bought. His house sits on an angle on the lot, which measures 80 feet by 80 feet. The boundaries of his house are described by the four equations below.
3x-4y=55
3x+2y=85
3x-4y=-125
3x+2y=175
The house faces southwest.
The fence will run from the farthest north corner of the house to 5, 80 and then run along the north lot line to the corner of the lot 80, 80. It will then head south on the lot line to 80, 30. From there it will angle toward the house to 55,5 and then head to the farthest east corner of the house.
A shade tree will be placed at the intersection of 3x-4y=55 and x+3y=170, while an ornamental tree will be placed 15 feet south of the west corner of the house.
Prepare a graph for the landscape workers to use as a guide. Follow these steps to organize your data.
· Determine how to set up the graph and its scale
· Construct a colorful and detailed graph that Gavin could give to the landscaper workers.
· Create the system of inequalities that describes Gavin’s fenced area.
· Determine the vertices of the house.
· Determine the vertices of the two trees.
Write a detailed description for the workers of the work that needs to be done and the area where the work is to be done.
Click here to see answer by solver91311(16877) |
Question 526295: Set up the following word problem as an equation or expression and solve. Then finish your response by answering the question in the word problem with a complete sentence.
After a 20% increase in patients, a clinic treated 240 patients per week. How many patients did the clinic see the week before the increase?
I got 100% on my 20 question math test on percentages/decimals/mixture problems and the like, but this problem goes right over my head. If you could simply map out the formula and explain why that would be awesome. I'm not looking for someone to do this work for me, just help me get it started.
Thank you!
Click here to see answer by scott8148(6628) |
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