1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Lynna [10]
2 years ago
13

A lawyer has found 60 investors for a limited partnership to purchase an inner-city apartment building, with each contributing e

ither $3,000 or $6,000. If the partnership raised $258,000, then how many investors contributed $3,000 and how many contributed $6,000?
x = $3,000 investors
y =
$6,000 investors

Formulate the situation as a system of two linear equations in two variables. Be sure to state clearly the meaning of your x- and y-variables. Solve the system by the elimination method. Be sure to state your final answer in terms of the original question.

A jar contains 70 nickels and dimes worth $5.70. How many of each kind of coin are in the jar?

Formulate the situation as a system of two linear equations in two variables. Be sure to state clearly the meaning of your x- and y-variables. Solve the system by the elimination method. Be sure to state your final answer in terms of the original question.

The concession stand at an ice hockey rink had receipts of $7400 from selling a total of 3000 sodas and hot dogs. If each soda sold for $2 and each hot dog sold for $3, how many of each were sold?

x= soda

y= hotdogs
Mathematics
1 answer:
kap26 [50]2 years ago
7 0

Answer:

1) There were 34 $3,000 investors and 26 $6,000 investors.

2) There are 26 nickels and 44 dimes in the jar.

3) 1600 sodas and 1400 hot dogs were sold.

Step-by-step explanation:

1) A lawyer has found 60 investors for a limited partnership to purchase an inner-city apartment building, with each contributing either $3,000 or $6,000. If the partnership raised $258,000, then how many investors contributed $3,000 and how many contributed $6,000?

x is the number of investors that contributed 3,000.

y is the number of investors that contributed 6,000.

Building the system:

There are 60 investors. So:

x + y = 60

In all, the partnership raised $258,000. So:

3000x + 6000y = 258000

Simplifying by 3000, we have:

x + 2y = 86

Solving the system:

The elimination method is a method in which we can transform the system such that one variable can be canceled by addition. So:

1)x + y = 60

2)x + 2y = 86

I am going to multiply 1) by -1, then add 1) and 2), so x is canceled.

1) - x - y = -60

2) x + 2y = 86

-x + x -y + 2y = -60 +86

y = 26

Now we get back to equation 1), and find x

x + y = 60

x = 60-y = 60-26 = 34

There were 34 $3,000 investors and 26 $6,000 investors.

2) A jar contains 70 nickels and dimes worth $5.70. How many of each kind of coin are in the jar?

I am going to say that x is the number of nickels and y is the number of dimes.

Each nickel is worth 5 cents and each dime is worth 10 cents.

Building the system:

There are 70 coins. So:

x + y = 70

They are worth $5.70. So:

0.05x + 0.10y = 5.70

Solving the system:

1) x+y = 70

2) 0.05x + 0.10y = 5.70

I am going to divide 1) by -10, so we can add and cancel y:

1) -0.1x -0.1y = -7

2) 0.05x + 0.1y = 5.70

-0.1x + 0.05x -0.1y + 0.1y = -1.3

-0.05x = -1.3 *(-100)

5x = 130

x = \frac{130}{5}

x = 26

Now:

x+y = 70

y = 70 - x = 70 - 26 = 44

There are 26 nickels and 44 dimes in the jar.

3) The concession stand at an ice hockey rink had receipts of $7400 from selling a total of 3000 sodas and hot dogs. If each soda sold for $2 and each hot dog sold for $3, how many of each were sold?

x is the nuber of sodas and y is the number of hot dogs.

Building the system:

3000 items were sold. So:

x + y = 3000

$7,4000 was the total price of these items. So:

2x + 3y = 7400

Solving the system:

1)x + y = 3000

2)2x + 3y = 7400

I am going to multiply 1) by -2, so we can cancel x

1) -2x -2y = -6000

2) 2x + 3y = 7400

-2x + 2x -2y + 3y = -6000 + 7400

y = 1400

Now, going back to 1)

x + y = 3000

x = 3000-y = 3000-1400 = 1600

1600 sodas and 1400 hot dogs were sold.

You might be interested in
is a 50 percent increase followed by a 33 1/2 percent decrease same less or greatter than the original value
Nitella [24]

Answer:less than

Step-by-step explanation:

3 0
3 years ago
Hector made some observations about the numbered cards before his friend turned them face down and rearranged them in a differen
Zarrin [17]

Answer:

c and e

Step-by-step explanation:

he cant get 2 and there are 8 cards and only one of them is a one

6 0
3 years ago
The arnold family arrived ar the beach at 10:30 A.M. Thay spent 3 3/4hours there. What time dud they leave the beach?
VMariaS [17]
The arnold family arrived at the beach at 10:30 A.M.

10:30 

Add 3 hours and 3/4 minutes to that

3/4 = 75% of 60

.75 * 60 = 45

3 hours and 45 minutes 

10:30 >> 3 hours more = 1:30
1:30 + 45 mins = 2:15

Answer would be: They left at 2:15


5 0
3 years ago
Read 2 more answers
Jakob rolls an 8-sided die that is numbered from 1 through 8 a total of 400 times. About how many times should Jakob expect to r
sergij07 [2.7K]
P(5 on one throw) = 1/8 
expected number of 5's in 400 throws = 1/8 * 400 = 50
3 0
2 years ago
Read 2 more answers
. How many minutes is it from 23:35 today to 01:15 tomorrow?
Aleksandr [31]

Answer:

A (100)

Step-by-step explanation:

If 2 hours pass starting at 23:35 today, then tomorrow the time will be 1:35. The difference between 1:35 and 1:15 is 20 (minutes) Because there are 120 minutes in 2 hours (60 minutes per hour), This means we do 120 minutes minus 20 minutes. This gives us an answer is A, 100 :)

5 0
2 years ago
Other questions:
  • Explain the steps in calculating the mean absolute deviation of a set of data.
    11·2 answers
  • Help please :) ! The dashed triangle is the image of the pre-image solid triangle. What is the scale factor used to create the d
    9·2 answers
  • Do you think it is okay to make friends over the internet or is it too dangerous to trust what people over the internet are sayi
    12·1 answer
  • Any help please? I need help :)
    10·1 answer
  • !!PLEASE ANSWER ASAP!!<br><br> is the relation a function?
    7·1 answer
  • I = $54, P = $800, r = 4.5%, What is the time
    5·1 answer
  • What is the consumer price index
    14·1 answer
  • DO NOT EXPLAIN WILL GIVE BRAINLIEST
    9·1 answer
  • 4/9
    9·1 answer
  • Please help I was supposed to do this yesterday <br><br> If x=-4 and y= 9/2
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!