Judy has $100 and Elenore has $75. Judy is saving $5 per day and Elenore is saving $7 per day.
give answers to all these questions below using the context of the sentence above
What equation represent how much money Judy will have in total after saving for D days?
What equation represents how much money Elenore will have in total after saving for D days?
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?
After the number of days it took both to have the same amount of money saved, how much money do they have each?
1) The equation that represents how much money Judy will have in total after saving for D days is: 100 + 5D.
2) The equation that represents how much money Elenore will have in total after saving for D days is: 75 + 7D.
3) The equation that would be used to find out how many days it will take for Judy and Elenore to have the same amount of money saved is: 100 + 5D = 75 + 7D.
4) After the number of days it took both to have the same amount of money saved, the amount of money they each have can be found by substituting the value of D into either Judy's or Elenore's equation.
To answer your questions using the given context:
1. The equation to represent how much money Judy will have in total after saving for D days is:
Total money Judy will have = 100 + (5 * D)
2. The equation to represent how much money Elenore will have in total after saving for D days is:
Total money Elenore will have = 75 + (7 * D)
3. The equation that would be used to find out how many days it will take for Judy and Elenore to have the same amount of money saved is:
100 + (5 * D) = 75 + (7 * D)
4. After the number of days it took for both Judy and Elenore to have the same amount of money saved, the total money they each have can be found by substituting the value of D into either of their equations. For example, if D is the number of days it took:
Judy's total money = 100 + (5 * D)
Elenore's total money = 75 + (7 * D)
To answer these questions, we need to understand the given information and use it to form equations.
1. How much money Judy will have in total after saving for D days?
Judy is saving $5 per day, so after D days she will have saved a total of $5 * D. To represent this in an equation, we can say:
Total amount of money Judy will have = $100 + ($5 * D)
2. How much money Elenore will have in total after saving for D days?
Elenore is saving $7 per day, so after D days she will have saved a total of $7 * D. To represent this in an equation, we can say:
Total amount of money Elenore will have = $75 + ($7 * D)
3. How many days it will take for Judy and Elenore to have the same amount of money saved?
To find the number of days it takes for Judy and Elenore to have the same amount of money saved, we need to set the two equations equal to each other and solve for D. The equations are:
$100 + ($5 * D) = $75 + ($7 * D)
4. After the number of days it took both to have the same amount of money saved, how much money do they have each?
Once we calculate the value of D from the previous equation, we can substitute that value into either of the original equations to find out how much money they have each.
Judy has $100 and Elenore has $75. Judy is saving $5 per day and Elenore is saving $7 per day.
give answers to all these questions below using the context of the sentence above
After the number of days it took both to have the same amount of money saved, how much money do they have each?
To find out how much money Judy and Elenore have each after they have the same amount of money saved, you would substitute the value of D (the number of days it took) into either Judy's or Elenore's equation.
Let's say it took D days for them to have the same amount of money saved. We can use the equation: Total amount of money Judy will have = $100 + ($5 * D) (or Total amount of money Elenore will have = $75 + ($7 * D))
After calculating the value of D, let's say it is 20, you would substitute this value into either equation:
Total amount of money Judy will have after 20 days = $100 + ($5 * 20) = $100 + $100 = $200
Total amount of money Elenore will have after 20 days = $75 + ($7 * 20) = $75 + $140 = $215
So, after 20 days, Judy will have $200 and Elenore will have $215.
Judy has $100 and Elenore has $75. Judy is saving $5 per day and Elenore is saving $7 per day.
After the number of days it took both to have the same amount of money saved, how much money do they have each?
options: 175, 15, 275, 162.50, 325
To find out how much money Judy and Elenore have each after they have the same amount of money saved, let's solve the equation we formed earlier:
Total amount of money Judy will have = Total amount of money Elenore will have
$100 + (5 * D) = $75 + (7 * D)
To solve for D, let's subtract $75 from both sides and then divide both sides by the difference in saving rate:
$100 - $75 = (7 * D) - (5 * D)
$25 = 2D
D = $25 / 2
D = 12.5
After 12.5 days, Judy and Elenore will have the same amount of money saved.
To calculate the amount of money they have each after 12.5 days, we can substitute D into either equation.
Total amount of money Judy will have = $100 + ($5 * 12.5) = $100 + $62.50 = $162.50
Total amount of money Elenore will have = $75 + ($7 * 12.5) = $75 + $87.50 = $162.50
So after 12.5 days, both Judy and Elenore will have $162.50 each.
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. Which equation would you use to solve this, where P = the number of pizza slices sold and S = the number of sodas sold?
options:
A 3.50P + 1.50S = 800 and P + S = 344
B 3.50S + 1.50P = 344 and P + S = 800
C 3.50S + 1.50P = 800 and P + S = 344
D 3.50P + S = 800 and P + 1.50S = 344
The correct equation to solve this problem is Option A: 3.50P + 1.50S = 800 and P + S = 344.
This is because the first equation represents the total revenue from selling pizza slices and sodas, which is made up of the price of pizza slices ($3.50) multiplied by the number of pizza slices sold (P), plus the price of sodas ($1.50) multiplied by the number of sodas sold (S), which should equal $800.
The second equation represents the total number of pizza slices and sodas sold, which is just the sum of the number of pizza slices (P) and the number of sodas (S), which should equal 344.
Select the statements that correctly describes the solution to this system of equations: 8x-2y=-4 and 4x-y=-2
options (choose all that apply):
A Solve this system by elimination since it is already in standard form and lined up nicely.
B There is exactly one solution to this system of linear equations and it is (2, 0).
C There are infinite solutions to this system of linear equations.
D These lines are parallel, so there is no solution to this system of linear equations.
E There is exactly one solution to this system of linear equations and it is (0, -2).
F Solve this system by substitution since one of the variables is defined by the other without having to do any math.
The correct statements that describe the solution to this system of equations are:
B There is exactly one solution to this system of linear equations and it is (2, 0).
F Solve this system by substitution since one of the variables is defined by the other without having to do any math.
The system of equations can be solved by substituting the value of y from one equation into the other equation. By doing so, we can solve for x and then substitute the value of x into either of the original equations to solve for y. This process will give us the unique solution (2, 0).
The other options are not correct for this system of equations:
A The system is not yet in standard form and elimination is not the appropriate method for solving this system.
C There are no infinite solutions as the system has a unique solution.
D The lines are not parallel, as the system has a solution.
E (0, -2) is not the correct solution to this system of 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?
options:
A Jim bought 15 begonias.
B Jim bought 18 begonias.
C Jim bought 4 petunias.
D Jim bought 15 petunias.
To solve this problem, we can set up a system of equations:
Let P represent the number of petunias bought and B represent the number of begonias bought.
The total number of potted plants bought can be represented by the equation: P + B = 19.
The total cost of the plants can be represented by the equation: 11P + 15B = 225.
To find the correct statement, we need to determine the values of P and B that satisfy both equations.
Solving the system of equations, we find that P = 9 and B = 10.
Therefore, the correct statement is: Jim bought 9 petunias.
None of the given options (A, B, C, or D) match the correct statement.
one of the given options HAS to give the correct statement, try again
Apologies for the confusion. Let's revisit the answer choices with the correct solution.
From the system of equations:
P + B = 19
11P + 15B = 225
The correct statement is:
Option D: Jim bought 15 petunias.
To confirm, let's substitute the value of P = 15 into the first equation:
15 + B = 19
B = 4
So, Jim bought 15 petunias and 4 begonias, which adds up to 19 plants in total.
add the system 6x+2y=60 and -6x-8y=-96 together
Adding the two equations:
(6x + 2y) + (-6x - 8y) = 60 + (-96)
Simplifying,
6x - 6x + 2y - 8y = 60 - 96
-6y = -36
Dividing both sides of the equation by -6:
y = 6
Therefore, the value of y is 6.
The Johnsons and the Wilsons went to the Burger Barn for dinner.
The Johnsons bought 2 burger meals and 5 hot dog meals for $46.
The Wilsons bought 5 burger meals and 2 hot dog meals for $52.
When you solve, you get a solution of (8, 6).
answer all the questions below
1, what does the 8 mean in context?
2, what does the 6 mean in context
3, who got the better deal?
1) In this context, the number 8 represents the cost of each burger meal. It means that each burger meal was priced at $8.
2) The number 6 represents the cost of each hot dog meal. It means that each hot dog meal was priced at $6.
3) To determine who got the better deal, we can compare the cost per meal for each family. The Johnsons paid $8 per burger meal and $6 per hot dog meal. The Wilsons paid $8 per burger meal and $6 per hot dog meal as well. Since the cost per meal is the same for both families, we can conclude that they both got the same deal and there is no clear better deal between the two.