When I went back to school and realized I was going to have to take math I was absolutely terrified. Before this class, I hadn't taken math since my junior year in high school. I was worried that I would quickly fall behind and really struggle. We started the class with the right triangle, and to my relief I caught on. With each new module I felt more confident and comfortable with math. In fact, I learned how fun it can be to solve a problem. It wasn't something that came instantly though. There was a lot of studying and watching math videos. By the end of the class many of my classmates saw me as a resource. They felt comfortable coming to me with their questions. I have felt a great sense of accomplishment by succeeding in a class I was afraid I would fail.
Working in the Yard Written Assignment
Story problems! Many of us shudder at the thought! In Math 1030 I was given a terribly complex story problem. With patience and a lot or work I was able to reason it through.
Here is the problem:
A neighbor of yours has a lawn that isn't looking too good. He has decided to remove all the old sod (grass), bring in a new 4 inch layer of topsoil, install new in-ground sprinklers, and reseed the lawn. He seems to think that he'll be able to save money by hauling loads of topsoil from the store himself in his pickup truck, rather than paying for delivery, but you’re not sure he's right. You're going to help him.
Is he redoing the whole yard or just the front?
He's redoing the whole yard
How much topsoil does he need?
I'm not sure, you'll have to figure that out. Remember he's putting a new 4 inch layer down over all the area currently covered by grass in the overhead picture above.
How big is the yard?
I'm not sure, but you can probably estimate it using the overhead picture.
What kind of pickup truck does he drive?
A 2003 Ford F-150 XL.
How much can the pickup carry?
The truck bed is 80 inches long, 69 inches wide, and 20 inches tall.
How much is the delivery charge?
$30 per truckload on top of the soil cost. Each truckload can deliver up to 18 cubic yards.
How much does the topsoil cost?
$18 per cubic yard (sold in 1/4 yard increments).
How far is the soil store?
It is 9 miles away. It takes about 20 minutes to drive there.
What gas mileage does the pickup truck get?
It averages 17 miles to the gallon.
What is the current gas cost?
Assume it's $3.79/gallon
In order to determine whether your neighbor will save money by picking up the soil himself you need to determine:
1. The area of the grass.
2. How much topsoil is needed.
3. How many trips the delivery truck will need to take.
4. How much it will cost to deliver the topsoil.
5. How much your neighbor's truck bed can carry in volume.
6. How many trips are needed with his pickup.
7. How many total miles will be driven with pickup.
8. The total cost of in gas to pick up topsoil.
You don't need to figure out how much the topsoil itself costs since it is a constant cost and will not change if delivered or picked up. To get the area of the grass you first need to calculate the total area of the yard. You then need to figure the area of the driveway and the area of the house. To do this you need to print off the map and pull out an old fashioned ruler. You first figure out how many cm=20 ft on the map. You physically measure the areas in CM and then convert to FT. Once you have the total area of the yard you subtract the area of the driveway and the house to get the area of the grass. You need four inches of topsoil. You take the area of the grass and times it by the depth of topsoil to get the volume of topsoil needed. Then, since the measurements are in feet you need to convert it to yards.You need 65.47 yards cubed of topsoil.
Next you need to figure out how many deliveries would need to be made. The truck delivers 18 cubic yards. You divide 65.47 by 18 to get 3.64 trips. Since the truck can't make partial trips you will need 4 deliveries of topsoil. $30 times 4=$120 to have the topsoil delivered.
Now that we have the cost of delivering the topsoil we need to figure the cost of picking up the soil. We need to find out how much the truck can carry per trip. The truck bed is 80" x 60" x 20" = 110,400 inches cubed. This is then converted to yards cubed for a total of 2.37 cubic yards that the truck bed can carry per trip. You then divide the topsoil need of c65.47 cubic yards by 2.37 cubic yards (truck bed capacity). This tells you that 27.62 trips are needed. We round this to 28 because you can't have a partial trip. It is 18 miles to drive to the store and back. The truck gets 17 MPG. Gas is 3.79/gallon. $3.79/17 MPG is about 0.22 per mile. 18 miles x 28 trips is 504 miles. 504 miles x .22 (cost of gas per mile) give you a total cost of $110.88. So, it is cheaper to pick up the soil b/c it is 110.88 in gas and it is $120 to have the soil delivered.
When you practically look at the problem though it is such a small savings. Your neighbor is going to spend a huge amount of time and energy pickup up and unloading the soil himself. Even though it is cheaper I would advise my neighbor to cough up the few extra bucks. His time is more valuable.
Here is the problem:
A neighbor of yours has a lawn that isn't looking too good. He has decided to remove all the old sod (grass), bring in a new 4 inch layer of topsoil, install new in-ground sprinklers, and reseed the lawn. He seems to think that he'll be able to save money by hauling loads of topsoil from the store himself in his pickup truck, rather than paying for delivery, but you’re not sure he's right. You're going to help him.
Is he redoing the whole yard or just the front?
He's redoing the whole yard
How much topsoil does he need?
I'm not sure, you'll have to figure that out. Remember he's putting a new 4 inch layer down over all the area currently covered by grass in the overhead picture above.
How big is the yard?
I'm not sure, but you can probably estimate it using the overhead picture.
What kind of pickup truck does he drive?
A 2003 Ford F-150 XL.
How much can the pickup carry?
The truck bed is 80 inches long, 69 inches wide, and 20 inches tall.
How much is the delivery charge?
$30 per truckload on top of the soil cost. Each truckload can deliver up to 18 cubic yards.
How much does the topsoil cost?
$18 per cubic yard (sold in 1/4 yard increments).
How far is the soil store?
It is 9 miles away. It takes about 20 minutes to drive there.
What gas mileage does the pickup truck get?
It averages 17 miles to the gallon.
What is the current gas cost?
Assume it's $3.79/gallon
In order to determine whether your neighbor will save money by picking up the soil himself you need to determine:
1. The area of the grass.
2. How much topsoil is needed.
3. How many trips the delivery truck will need to take.
4. How much it will cost to deliver the topsoil.
5. How much your neighbor's truck bed can carry in volume.
6. How many trips are needed with his pickup.
7. How many total miles will be driven with pickup.
8. The total cost of in gas to pick up topsoil.
You don't need to figure out how much the topsoil itself costs since it is a constant cost and will not change if delivered or picked up. To get the area of the grass you first need to calculate the total area of the yard. You then need to figure the area of the driveway and the area of the house. To do this you need to print off the map and pull out an old fashioned ruler. You first figure out how many cm=20 ft on the map. You physically measure the areas in CM and then convert to FT. Once you have the total area of the yard you subtract the area of the driveway and the house to get the area of the grass. You need four inches of topsoil. You take the area of the grass and times it by the depth of topsoil to get the volume of topsoil needed. Then, since the measurements are in feet you need to convert it to yards.You need 65.47 yards cubed of topsoil.
Next you need to figure out how many deliveries would need to be made. The truck delivers 18 cubic yards. You divide 65.47 by 18 to get 3.64 trips. Since the truck can't make partial trips you will need 4 deliveries of topsoil. $30 times 4=$120 to have the topsoil delivered.
Now that we have the cost of delivering the topsoil we need to figure the cost of picking up the soil. We need to find out how much the truck can carry per trip. The truck bed is 80" x 60" x 20" = 110,400 inches cubed. This is then converted to yards cubed for a total of 2.37 cubic yards that the truck bed can carry per trip. You then divide the topsoil need of c65.47 cubic yards by 2.37 cubic yards (truck bed capacity). This tells you that 27.62 trips are needed. We round this to 28 because you can't have a partial trip. It is 18 miles to drive to the store and back. The truck gets 17 MPG. Gas is 3.79/gallon. $3.79/17 MPG is about 0.22 per mile. 18 miles x 28 trips is 504 miles. 504 miles x .22 (cost of gas per mile) give you a total cost of $110.88. So, it is cheaper to pick up the soil b/c it is 110.88 in gas and it is $120 to have the soil delivered.
When you practically look at the problem though it is such a small savings. Your neighbor is going to spend a huge amount of time and energy pickup up and unloading the soil himself. Even though it is cheaper I would advise my neighbor to cough up the few extra bucks. His time is more valuable.