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Judy has $100 and Elenore has $75. Judy is saving $5 per day and Elenore is saving $7 per day. (4 points)

What equation represents how much money Judy will have in total after saving for d days? (response area )

What equation represents how much money Elenore will have in total after saving for d days? (response area 2)


What equation would be used to find out how many days it will take for Judy and Elenore to have the same amount of money saved? (response area 3)

After the number of days it took both to have the same amount of money saved, how much money do they have each? (response area 4)

1 responses
y = 5d + 100
y = 5d +75
y = 7d + 75
y = 100d + 5
y = 7d + 100
y = 75d + 7
y = 100d + 75

2 responses
y = 5d + 100
y = 5d +75
y = 7d + 75
y = 100d + 5
y = 7d + 100
y = 75d + 7
y = 100d + 75

3 responses
5d + 100 = 7d + 75
7d + 5d = 100 + 75
100d + 5 = = 75d + 7

4 responses
$162.50
$15
$175
$325
$275

11 answers

Let's break down the responses based on the information provided:

  1. Equation for Judy's savings after d days:

    • Judy starts with $100 and saves $5 per day. Thus, the equation representing how much money Judy will have is: \[ y = 5d + 100 \] (This is the first response area.)

  2. Equation for Elenore's savings after d days:

    • Elenore starts with $75 and saves $7 per day. Therefore, the equation representing how much money Elenore will have is: \[ y = 7d + 75 \] (This is the second response area.)

  3. Equation to find how many days it will take for Judy and Elenore to have the same amount of money saved:

    • To find out when they have the same amount saved, we can set their equations equal to each other: \[ 5d + 100 = 7d + 75 \] (This is the third response area.)

  4. Calculating how much money they both have after the calculated number of days:

    • Let's first solve for d in the equation \(5d + 100 = 7d + 75\):
      • Rearranging it gives: \[ 100 - 75 = 7d - 5d \] \[ 25 = 2d \] \[ d = 12.5 \]

    Now, substitute \(d = 12.5\) back into Judy's and Elenore's equations to find out how much each has:

    • For Judy: \[ y = 5(12.5) + 100 = 62.5 + 100 = 162.5 \]

    • For Elenore: \[ y = 7(12.5) + 75 = 87.5 + 75 = 162.5 \]

Thus, after the number of days it took both to have the same amount of money saved:

  • Judy and Elenore both have $162.50.

Now let’s summarize the responses accurately:

1: \(y = 5d + 100\)
2: \(y = 7d + 75\)
3: \(5d + 100 = 7d + 75\)
4: $162.50

The solution to a system of two linear equations is x = 3 weeks; y = 9 feet

Match the description with the correct statement.

(3 points)
How would you locate the solution of the two linear graphs on the coordinate plane?
How could you get exactly two or three solutions to this linear system?
The solution to this system could possibly have this meaning.

responses
find the point where the two lines cross; (3, 9)
making the lines parallel to each other
the point showing after 3 weeks, the plant was 9 feet tall
the point where the 9 foot tall plant stopped growing for 3 weeks
the point where the lines cross the y-axis after 3 weeks
no way to have 2 linear graphs with 2 or 3 intersecting points
from the origin, did the y-intercepts and subtract them
curving the lines around so that they cross multiple times

Let's match the descriptions with the correct statements based on the context of solving a system of two linear equations.

  1. How would you locate the solution of the two linear graphs on the coordinate plane?

    • Response: find the point where the two lines cross; (3, 9)

  2. How could you get exactly two or three solutions to this linear system?

    • Response: no way to have 2 linear graphs with 2 or 3 intersecting points (because two linear equations can only intersect at most once unless they are the same line or parallel)

  3. The solution to this system could possibly have this meaning.

    • Response: the point showing after 3 weeks, the plant was 9 feet tall

So the final matched statements are:

  1. Find the point where the two lines cross; (3, 9)
  2. No way to have 2 linear graphs with 2 or 3 intersecting points
  3. The point showing after 3 weeks, the plant was 9 feet tall
How could you check to see if the point (5, 6) is the solution to the Linear System of equations?(1 point)
Responses

Substitute 5 in for x and 6 in for y in both of the equations to see if both equations are true.
Substitute 5 in for x and 6 in for y in both of the equations to see if both equations are true.

Substitute 5 in for x and 6 in for y in one of the equations to see if the equation is true.
Substitute 5 in for x and 6 in for y in one of the equations to see if the equation is true.

Substitute 6 in for x and 5 in for y in one of the equations to see if the equation is true.
Substitute 6 in for x and 5 in for y in one of the equations to see if the equation is true.

Substitute 6 in for x and 5 in for y in both of the equations to see if both equations are true.

To check if the point (5, 6) is a solution to a system of linear equations, you need to determine whether it satisfies both equations.

The correct response is:

Substitute 5 in for x and 6 in for y in both of the equations to see if both equations are true.

This process will confirm if (5, 6) is indeed the solution by checking if both equations hold true when those values are substituted.

You are running a concession stand at a baseball game.

You are selling pizza slices and sodas.

Each pizza slice sells for $3.50 and each soda sells for $1.50.

At the end of the night, you made a total of $800.

You sold a total of 344 pizza slices and sodas combined.

You must report the number of pizza slices sold and the number of sodas sold.

What equations did you use to solve this, where P = the number of pizza slices sold and S = the number of sodas sold?

(1 point)
Responses

3.50P + S = 800 and P + 1.50S = 344
3.50P + S = 800 and P + 1.50S = 344

3.50P + 1.50S = 800 and P + S = 344
3.50P + 1.50S = 800 and P + S = 344

3.50S + 1.50P = 344 and P + S = 800
3.50S + 1.50P = 344 and P + S = 800

3.50S + 1.50P = 800 and P + S = 344

To determine the number of pizza slices and sodas sold at your concession stand, you can set up the system of equations based on the information provided.

You have two main pieces of information:

  1. The total sales amount is $800.
  2. The total number of items sold (pizza slices and sodas) is 344.

Let:

  • \( P \) = number of pizza slices sold
  • \( S \) = number of sodas sold

Based on the prices:

  • Each pizza slice sells for $3.50, so the total revenue from pizza slices is \( 3.50P \).
  • Each soda sells for $1.50, so the total revenue from sodas is \( 1.50S \).

The equations that can be set up are:

  1. Total revenue equation: \( 3.50P + 1.50S = 800 \)
  2. Total items sold equation: \( P + S = 344 \)

Therefore, the correct response is:

3.50P + 1.50S = 800 and P + S = 344

Check all that apply. Select the statement(s) that correctly describes the solution to this system of equations:

8x−2y=−4

4x−y=−2

(2 points)
Responses

Solve this system by elimination since it is already in standard form and lined up nicely.
Solve this system by elimination since it is already in standard form and lined up nicely.

There is exactly one solution to this system of linear equations and it is (2, 0).
There is exactly one solution to this system of linear equations and it is (2, 0).

There are infinite solutions to this system of linear equations.
There are infinite solutions to this system of linear equations.

These lines are parallel, so there is no solution to this system of linear equations.
These lines are parallel, so there is no solution to this system of linear equations.

There is exactly one solution to this system of linear equations and it is (0, -2).
There is exactly one solution to this system of linear equations and it is (0, -2).

Solve this system by substitution since one of the variables is defined by the other without having to do any math.
Solve this system by substitution since one of the variables is defined by the other without having to do any math.
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To analyze the system of equations and determine the correct statements, let's first simplify and solve the provided equations:

  1. Equations:

    • \( 8x - 2y = -4 \)
    • \( 4x - y = -2 \)

  2. Solving the first equation for y: We can rearrange the first equation: \[ 8x - 2y = -4 \ -2y = -4 - 8x \ 2y = 8x + 4 \ y = 4x + 2 \]

  3. Substituting into the second equation: Now plug \( y = 4x + 2 \) into the second equation: \[ 4x - (4x + 2) = -2 \ 4x - 4x - 2 = -2 \ -2 = -2 \] Since this is always true (an identity), it indicates that the two equations are actually the same line.

  4. Conclusion: This means there are infinite solutions to the system of equations.

Now, let’s evaluate the responses based on this analysis:

  1. Solve this system by elimination since it is already in standard form and lined up nicely.

    • Response: Correct (Elimination can be done, but it may not be necessary since the equations are equivalent.)

  2. There is exactly one solution to this system of linear equations and it is (2, 0).

    • Response: Incorrect (There is not just one solution; there are infinitely many.)

  3. There are infinite solutions to this system of linear equations.

    • Response: Correct (This is true because the two equations represent the same line.)

  4. These lines are parallel, so there is no solution to this system of linear equations.

    • Response: Incorrect (The lines are not parallel; they are the same line.)

  5. There is exactly one solution to this system of linear equations and it is (0, -2).

    • Response: Incorrect (Again, there are infinitely many solutions, not just one.)

  6. Solve this system by substitution since one of the variables is defined by the other without having to do any math.

    • Response: Incorrect (While substitution can be used, it does require some manipulation to express y clearly.)

Correct Responses Summary:

  • Solve this system by elimination since it is already in standard form and lined up nicely.
  • There are infinite solutions to this system of linear equations.
Jim bought some potted plants:

Petunias cost $11 per pot and Begonias cost $15 per pot.

Jim bought 19 potted plants in all and spent a total of $225 on the plants.

Which would be a correct statement?

(1 point)
Responses

Jim bought 4 petunias.
Jim bought 4 petunias.

Jim bought 18 begonias.
Jim bought 18 begonias.

Jim bought 15 petunias.
Jim bought 15 petunias.

Jim bought 15 begonias.

To determine how many petunias and begonias Jim bought, we can set up a system of equations. Let:

  • \( P \) = the number of petunias
  • \( B \) = the number of begonias

We have the following information:

  1. Jim bought a total of 19 plants: \[ P + B = 19 \]

  2. Jim spent a total of $225 on the plants: \[ 11P + 15B = 225 \]

Now, we can solve this system of equations.

Step 1: Solve for one variable

From the first equation: \[ B = 19 - P \]

Step 2: Substitute into the second equation

Substituting \( B \) into the second equation: \[ 11P + 15(19 - P) = 225 \] Expanding this gives: \[ 11P + 285 - 15P = 225 \] Combine like terms: \[ -4P + 285 = 225 \] Subtract 285 from both sides: \[ -4P = 225 - 285 \ -4P = -60 \] Divide by -4: \[ P = 15 \]

Step 3: Solve for \( B \)

Now, substitute \( P \) back into the equation for \( B \): \[ B = 19 - 15 = 4 \]

Conclusion

Jim bought 15 petunias and 4 begonias.

Given the responses:

  • Jim bought 4 petunias. (Incorrect)
  • Jim bought 18 begonias. (Incorrect)
  • Jim bought 15 petunias. (Correct)
  • Jim bought 15 begonias. (Incorrect)

The correct statement from the responses provided is:

Jim bought 15 petunias.