Creating Equations
Write an equation that represents the sentence "the sum of two unknown numbers is 18."
x + y = 18
(May use other variables)
Jenny buys two bags of chips for x dollars each and 5 drinks for y dollars each. She spends a total of $19. She represents this situation with the equation below:
2x + 5y = 19
The point (2.50, 2.80) is a solution to this equation. Interpret this solution in context.
In order for Jenny's purchase to cost $19, chips could cost $2.50 and drinks could cost $2.80.
(or something similar)
Is (1, 1) a solution to the system below? You must show your work to get credit!
x + y = 2
-x + 8y = 7
Yes
1 + 1 = 2
-(1) + 8(1) = 7
Jeremy will mow his neighbor's lawn for h hours at a rate of $6 an hour. Write an inequality that represents how many hours he needs to work to make more than $24.
6h > 24
What is the median of the following numbers?
1, 1, 5, 6, 9, 10, 18
Median: 6
If h represents a number, write an equation that shows "Sixty more than 9 times a number is 375".
9h + 60 = 375
Jenny buys two bags of chips for x dollars each and 5 drinks for y dollars each. She spends a total of $19. She represents this situation with the equation below:
2x + 5y = 19
The point (2.50, 3) is not a solution to this equation. Interpret this point in context.
If chips cost $2.50 and drinks cost $3, Jenny's purchase would not cost $19. (It would cost more)
(or something similar)
You graph a system of equations and the lines are parallel to each other (have the same slope but different y-intercepts). How many solutions does the system have?
No solutions.
Write an inequality to represent this statement: 2 more than w is less than or equal to 15.
w + 2 ≤ 15
3x + 5 = 23
3x – 7 = 11
Yes.
The two equations have the same solution (x = 6).
The two equations can be transformed into the same equation.
3x + 5 – 5 = 23 – 5 gives you 3x = 18.
3x – 7 + 7 = 11 + 7 gives you 3x = 18.
An online streaming service charges a one-time activation fee of $3.95. Each additional month of use costs $4.50. Write an equation that gives C, the total cost of the streaming service, after m months.
C = 4.50m + 3.95
The equation C = 1.50m + 2.40 represents the cost of a taxi ride that costs $1.50 per mile and $2.40 in bridge tolls.
Interpret the solution (3, 6.90) in context.
If you take the taxi for 3 miles, the total cost will be $6.90.
Below is a system of equations.
x – 6y = 12
y = 2 + x
Write an equation that represents a correct substitution of the second equation into the first.
x – 6(2 + x) = 12
Trevor spends $2 each on x notebooks and buys a backpack for $15. Write an inequality to represent the number of notebooks Trevor can buy and spend at most $27.
2x + 15 ≤ 27
What is the average of the following numbers?
1, 1, 7, 11
For an EXTRA 300 points: How does the average change if we add the number 10 into the data set?
Average:5
With 10, the average is 6 (the average increases by 1)
Mari needed prizes for her class. She bought x bags of mixed chocolate for $9.85 each and y bags of skittles for $6.50 each. She spent a total of $58.90. Represent Mari's purchase with an equation.
9.85x + 6.50y = 58.90
The equation C = 1.50m + 2.40 represents the cost of a taxi ride that costs $1.50 per mile and $2.40 in bridge tolls.
Is (10, 17.50) a solution to the equation? Interpret your answer in context.
No
1.50(10) + 2.40 is equal to 17.40, not 17.50.
If you take the taxi for 10 miles, the total cost is not 17.50.
6x – 4y = 12
2x + y = 1
3 ( 2x + y = 1 )
6x + 3y = 3
Jenny buys two giftcards for x dollars each and pays a $1 fee for each card. She spends a minimum of $52.
2(x + 1) ≥ 52
OR
2x + 2 ≥ 52
Is (8, 1) a solution to the inequality below? Explain or show your work.
y + 5 ≥ 10 – x
Yes.
(8, 1) --> x = 8 and y = 1
1 + 5 ≥ 10 – 8
6 ≥ 2
For a class picnic, two teachers went to the same store to purchase drinks. One teacher purchased 18 juice boxes and 32 bottles of water, and spent $19.92. The other teacher purchased 14 juice boxes and 26 bottles of water, and spent $15.76.
Write a system of equations to represent the costs of a juice box, j, and a bottle of water, w.
18j + 32w = 19.92
14j + 26w =15.76
At a bodega, sandwiches take 3 minutes each to make and smoothies take 2.5 minutes each to make. The equation 3x + 2.5 = 11.50 represents the time it took for Julio to get his bodega order.
Each question is worth 250 points:
1. What does x represent in this situation?
2. How many smoothies did Julio buy at the bodega?
1. x represents the number of sandwiches Julio bought.
2. Julio bought one smoothie. The 2.5 in the equation represents the wait time for this one smoothie.
Find the value of x in the system below by eliminating the y terms.
2x – 8y = 1
3x + 8y = 14
2x – 8y = 1
+ ( 3x + 8y = 14 )
5x = 15
x = 3
At a museum, a group rate of $340 plus $2 per student is cheaper than an individual rate of $12 per student. Let s be the number of students.
340 + 2s < 12s
Graph the inequality 1/2x + y > 5.
In slope-intercept form: y > -1/2x + 5
y-intercept: 5
slope: -1/2
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