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Creating Systems of Equations from word problems

LorenaJac

New member
Joined
Oct 19, 2017
Messages
1
I have to create a system of equations for each of these problems and I can't seem to figure them out. If someone could help, that would be great! Thank you.



Problem number 1 - I want to be clear on how much we will be getting back in annual return. We are planning to invest $20,000 in two different accounts. The first is a high risk account that earns 10% annual interest and the second is a low risk account that earns 5% annual interest. We would like to earn 8% total interest. How much should we invest in each account? I will need the full details with all the calculations for my files.
Problem number 2 - As we discussed on the phone, we will need 200 pounds of premium South American coffee at $6.98 a pound. We need this order immediately and I understand that you do not have that type of coffee in stock. However, you explained that you could make that mixture of coffee by blending Brazilian coffee that costs $9.20 per pound with Columbian coffee that costs $5.50 per pound. How many pounds of each kind will be used? I will need the full details with all the calculations for my files.

Problem 3 - I see that you have both a high risk and a low risk mutual fund. If you invest $4000 in the low risk and $5000 in the high risk, the total income is $750. If you invest $8000 in the low risk and $9000 in the high risk, the total income is $1390. I am interested in finding out the percent return for both the low risk and the high risk funds. I have many senior citizens who wish to invest with you, but they need to know those percent amounts in writing before they consider investing thousands of dollars with your company.

Problem 4 -
Our records reflect that over the past month, we received shipments of recorders and harmonicas from Instrument Supply Warehouse. The shipment containing 5 recorders and 4 harmonicas cost $62. A second shipment containing 10 recorders and 3 harmonicas cost $84. For future reference, we would like to know how much each instrument costs. In other words, what is the cost of a recorder? And, what is the cost of a harmonica?


Problem 5 - I want to be clear as to how many vehicles we will need. Your luxury busses will hold 45 skiers and their equipment. Your vans will hold 5 skiers and their equipment. We expect to have 195 skiers participating in this much anticipated trip. A bus costs $350 to rent for the trip and a van costs $115 to rent for the trip. The North Haven Ski Club has $1745 to use for transportation. At your earliest convenience, would you please let me know how many busses and how many vans we will need for this trip?
 

tkhunny

Moderator
Staff member
Joined
Apr 12, 2005
Messages
9,701
Well, it's very difficult to help if we don't know what you've done. Please show your work.

Rule of Thumb: If you don't know what it is, then give it name.

***** Example *****

Question: How many apples are there?
Answer: That's what I'm supposed to find out!
Reaction: A = The number of apples.
 

stapel

Super Moderator
Staff member
Joined
Feb 4, 2004
Messages
15,937
I have to create a system of equations for each of these problems and I can't seem to figure them out. If someone could help, that would be great! Thank you.

Problem number 1 - I want to be clear on how much we will be getting back in annual return. We are planning to invest $20,000 in two different accounts. The first is a high risk account that earns 10% annual interest and the second is a low risk account that earns 5% annual interest. We would like to earn 8% total interest. How much should we invest in each account? I will need the full details with all the calculations for my files.

Problem number 2 - As we discussed on the phone, we will need 200 pounds of premium South American coffee at $6.98 a pound. We need this order immediately and I understand that you do not have that type of coffee in stock. However, you explained that you could make that mixture of coffee by blending Brazilian coffee that costs $9.20 per pound with Columbian coffee that costs $5.50 per pound. How many pounds of each kind will be used? I will need the full details with all the calculations for my files.

Problem 3 - I see that you have both a high risk and a low risk mutual fund. If you invest $4000 in the low risk and $5000 in the high risk, the total income is $750. If you invest $8000 in the low risk and $9000 in the high risk, the total income is $1390. I am interested in finding out the percent return for both the low risk and the high risk funds. I have many senior citizens who wish to invest with you, but they need to know those percent amounts in writing before they consider investing thousands of dollars with your company.

Problem 4 - Our records reflect that over the past month, we received shipments of recorders and harmonicas from Instrument Supply Warehouse. The shipment containing 5 recorders and 4 harmonicas cost $62. A second shipment containing 10 recorders and 3 harmonicas cost $84. For future reference, we would like to know how much each instrument costs. In other words, what is the cost of a recorder? And, what is the cost of a harmonica?

Problem 5 - I want to be clear as to how many vehicles we will need. Your luxury busses will hold 45 skiers and their equipment. Your vans will hold 5 skiers and their equipment. We expect to have 195 skiers participating in this much anticipated trip. A bus costs $350 to rent for the trip and a van costs $115 to rent for the trip. The North Haven Ski Club has $1745 to use for transportation. At your earliest convenience, would you please let me know how many busses and how many vans we will need for this trip?
To learn how to set up and solve system-of-equation word problems, please try here. (Note: The lessons at the link assume that you know how to work with variables and how to "translate English into algebra.)

After you have studied at least two lessons, please attempt the posted exercises. If you get stuck, you can then reply with a clear listing of your thoughts and efforts, at which point we can respond with useful helps and hints. Thank you! ;)
 
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