You sell candy bars (c = # of candy bars sold) for $1.50 each and wristbands (w = # of wristbands sold) for $2.00 each. You made $10. You sold 6 items.
1.5c + 2w = 10
c + w = 6
100
Popcorn (p = # of popcorn you could buy) is $2 and cotton candy (c = # of cotton candy you could buy) is $3. You have $10 in your pocket to spend.
2p + 3c ≤ 10
100
y ≤ 4x - 3
Solid line / shade below
100
Parallel lines
No solution
200
x = 2y - 3
3x - 4y = - 2
Substitution. The first x is already isolated.
200
You sell flowers (f = # of flowers sold) for $3.25 each and ribbons (r = # of ribbons sold) for $1.75 each. You made $19.75. You sold 7 items.
3.25f + 1.75r = 19.75
f + r = 7
200
Hardback books (h = # of hardback books you could buy) are $4 each and paperback books (p = # of paperback books you could buy) are $2.50 each. You have to spend less than $20.
4h + 2.5p < 20
200
y > 2x - 6
Dashed line / shade above
200
Two lines intersect at one point
One solution
300
y = 2x + 3
y = 3/2x - 4
Graphing. They are both in slope intercept form (y = mx + b)
300
You sell water bottles (w = # of water bottles sold) for $1.00 each and cans of soda (s = # of cans of soda sold) for $0.50 each. You made $100. You sold 125 items.
w + .5s = 100
w + s = 125
300
You sold candy bars (c = # of candy bars sold) for $1.00 each and wristbands (w = # of wristbands sold) for $2.00 each. You have to make at least $15 today.
c + 2w ≥ 15
300
2x + y ≤ 4
Solid line / shade below
300
x = 2 ; y = 8 (2, 8)
One solution
400
14x - y = 12
9x + y = 5
Elimination. The y's will eliminate.
400
It takes you 180 minutes to wash 2 trucks (t = time to wash a truck) and 5 cars (c = time to wash a car). It takes you 120 minutes to wash 2 trucks and 3 cars.
2t + 5c = 180
2t + 3c = 120
400
A garage sale sells items for $3 or $6 each. You have $24 to spend.
3x + 6y ≤ 24
400
x > 9
Dashed line / shade above (right)
400
0 = 0
Infinite solutions
500
2x + y = 3
6x + 4y = 10
Elimination or substitution. You could multiply the first equation by either -3 or -4 to get the x's or y's to eliminate, respectively. You could also solve for y in the first equation in one step in order to substitute.
500
You sell sundaes (s = # of sundaes sold) for $2.25 and ice cream cones (i = # of ice cream cones sold) for $1.75. You made $45.50. You sold 6 more sundaes than ice cream cones.
2.25s + 1.75i = 45.5
s = 6 + i
500
You are having a garage sale. You are selling items for $0.25 and $5 each. You want to make more than $50.