Word Problems (Set Up)
Harold bought 4 pens and 3 pencils for $10. Jake bought 2 pens and 1 pencil for $4. Write a system of equations to represent this scenario.
4x + 3y = 10
2x + 1y = 4
The sum of Ben’s age and Tony’s age is 21 years. The difference between their ages is 9. Ben is older than Tony. How old is Tony?
6 years old
-x + 2y = -15
8x - 2y = -20
(-5, -10)
y < (1/2)x - 2
dotted line
shade BELOW
What symbols indicate a solid line?
>= and <=
The basketball game brought in a total of $550 last night by selling a total of 75 tickets. Student tickets (s) were sold for $5 and adult tickets (a) were sold for $10. Write 2 equations to model this situation.
s + a = 75
5s + 10a = 550
Leonardo bought 1 soda and 1 popcorn for $9. Diane bought 3 sodas and 2 popcorns for $20. How much is one popcorn?
$7.00
-6x - 10y = -18
-3x + 10y = 36
(-2, 3)
y > -2x + 1
dotted line
shade above
Where can you find the solution(s) to a system of inequalities?
Where the shaded regions overlap!!
Caleb scored a total of 37 points last night by making a total of 20 baskets. Some baskets were 1-point free throws (f), and the rest were 2-point field goals (g). Write 2 equations to model this situation.
f + g = 20
f + 2g = 37
Garrett and Camille each have $10. Garrett spends all his money and buys 3 hardcover books and 4 softcover books. Camille spends $8 and buys 3 hardcover books and 2 softcover books. What is the cost of 1 hardcover?
$2.00
-x + 3y = -15
3x + 3y = 21
(9, -2)
y > 5
horizontal line
dotted line
shade ABOVE
y < x - 3
y > -x + 1
dotted below
dotted above
Charity bought a total of 5 items at Sheetz for $6.50. Each candy bar cost $1 and each drink cost $1.50. Write a system of equations to find the number of candy bars (c) and the number of drinks (d) she bought.
c + d = 5
1c + 1.50d = 6.50
Sarah bought 2 drinks and 2 hamburgers for $10. Diane bought 3 drinks and 1 hamburger for $8. How much is one hamburger?
$3.50
-3x + 4y = 12
2x + 2y = -22
(-8, -3)
x < -2
Vertical line
dotted line
shade left
y > (1/2)x + 1
x + y < 2
1st line dotted and shade above
2nd dotted and shade BELOW
Andy watched a total of 10 movies and tv episodes this weekend, which totaled 14 hours of television. Each movie was 2 hours long and each show was 0.5 hours long. Write a system of equations to find the number of movies (m) and the number of shows (s) he watched.
m + s = 10
2m + .5s = 14
Calen and Tayshia each have $12.50. Calen spends all his money and buys 2 CD and 3 DVDs. Tayshia spends $8.50 and buys 2 CDs and 1 DVD. What is the cost of 1 CD?
$3.25
4x + 3y = -14
8x + 10y = -36
(-2, -2)
2x + 2y < 4
* y < -x + 2
* dotted line
* BELOW
2x + 2y < 4
6x - 3y > 3
Both lines dotted and shaded BELOW
y < -x + 2
y < 2x - 1