Model Citizens
A teacher creates an assignment worth 50 points using x 2-point questions and y 5-point questions. This is the equation representing the point total.
3x+5y=50
The total time, in minutes, Marcus needs to stuff 600 event invitation envelopes if he works at a rate of 12 envelopes per minute.
50 minutes
In the crate weight equation W = 400 + 85.5J, the ordered pair (8, 1084) represents this scenario.
What is "A crate containing 8 glass jars has a total weight of 1,084 grams"
A train travels 900 miles from Chicago to Denver. If x is miles traveled from Chicago and y is miles remaining to Denver, x + y always equals this.
900 miles
Is x = 5 a solution to the equation 4x - 7 = 13?
Yes
A screen printing shop charges $12 per custom hoodie (H) plus a setup fee of $75 for each distinct ink color (C). This equation yields total cost (W).
W = 12T + 75C?
The number of minutes Marcus saves on his 600-envelope task if he increases his stuffing speed from 12 to 20 envelopes per minute.
Original: 600 event invitation envelopes if he works at a rate of 12 envelopes per minute.
20 mins
On the juice budget line 4a + 2.50c = 80, the coordinate point (10, 16) represents this combination.
What is buying 10 gallons of apple juice and 16 gallons of cranberry juice for $80?
On a 1200-mile route from Minneapolis to New Haven, a train is 350 miles out of New Haven. This is its distance remaining to Minneapolis.
What is 550 miles
Is the coordinate point (3, 4) a solution to the two-variable equation 2x + 3y = 15?
NO!
You have a budget of $80 to buy apple juice (a) at $4 per gallon and cranberry juice (c) at $2.50 per gallon. This equation models your spending limit.
4a + 2.50c = 80
An equation representing the time t in minutes to stuff 600 envelopes at a constant rate of r envelopes per minute.
t = 600/r
The y intercept of 4a + 2.50c = 80 is (0, 32). This is what it means in terms of the party drinks.
What is buying 0 gallons of apple juice and 32 gallons of cranberry juice
As distance covered from Alaska (x) increases by 150 miles, the remaining distance to Denver (y) changes how by this amount.
decreases by 150
Is the ordered pair (2, -1) a valid solution to the inequality 5x - 2y < 12
No
In the wooden crate weight equation W = 400 + 85.5J, the constant 400 represents this physical measurement in grams.
What is the weight of the empty crate?
Reggie finishes labeling all 1000 books in exactly 100 minutes without taking breaks. This was her labeling speed in books per minute.
10 books per min
If you purchase 12 gallons of apple juice using 4a + 2.50c = 80, this is the exact number of gallons of cranberry juice you can afford.
What is 12.8 gallons?
For a 900-mile plane trip, this equation models remaining distance y as a function of covered distance x.
y = 900 - x
Is (3, 2) a solution to the system of equations: x + y = 5 AND 30x - 20y = 50?
Yes
A drama club orders 40 custom masks at $5 each plus a mold setup fee of $45 per color design. At 3 colors, this is the total bill.
What is $335
A basketball player needs to score 1000 points before he leaves the gym at practice. If he scores 200 free throws and 100 layups, how many 3 pointers would he need? Set up a valid equation.
3x+2y+1z=1000 .. 200 3pts
A filled shipping crate following W = 400 + 85.5J has a total mass of 1,255 grams. This is how many glass jars are inside.
10 jars
The ordered pair (x, y) representing the location when the train has completed exactly one-third of its 900-mile trip toward Denver.
(300,600)
A budget constraint for a GIANT pasta party is 2x + 0.50y < 140, where x is pounds of pasta and y is pounds of sauce, Is buying 50 lbs of pasta and 50 lbs of sauce a valid solution?
Yes