Equations
Inequalities
Proportional Relationships
Rates, Ratios, Proportions
Word Problems
100
-3x + 6 = -21
x = 9
100
x/8 - 5 < -10
x < -40
100
Is this a direct proportion?
If so, what is the constant?
What is the direct proportion equation?
Yes
k = 3
y=3x
100
7/9 = x/72
x = 56
100
Alli had three times as much as Sarah. Laura had $12 more than Sarah. Together, they have $77. How much money did each girl raise?
Alli: $39
Laura: $25
Sarah: $13
200
12x - 4 - 16x = 20
x = -6
200
-4x + 7 < 23
x > -4
200
Describe the two ways to tell whether a graph shows a proportional relationship or not.
1) The line passes through the origin.
2) It is linear (a straight line).
200
Ms. Collins reads 246 pages in 3 hours. How many pages does she read per hour?
82 pages per hour
200
Mark went to the boardwalk with $22 to spend. The admission into the boardwalk was $4. Each game cost $2.10. At most, how many games can Mark play?
At most, Mark can play 8 games.
x is less than or equal to 8 games.
300
x/9 = -42
x = -378
300
3.4 + x/2 > 17.4
x > 28
300
Is this a direct proportion?
If yes, what is the constant?
What is the direct proportion equation?
Yes
k=1/2
y=1/2x
300
There are 16 basketballs, 13 baseballs, 9 footballs, and 15 softballs.
Write a simplified ratio of footballs to basketballs AND softballs.
9:31
300
The sum of 3 consecutive integers is 144. What are the three numbers?
47, 48, 49
400
1/2(16x - 10) = 27
x = 4
400
5/6x + 4 - 1/2x > 17
x > 39
400
What is the constant?
A
k=9
400
Ms. Linzenbold and her family took a road trip last weekend. They drove 786 miles in 12 hours. What was Ms. Linzenbold's average speed?
65.5 miles per hour
400
In the basketball game, Ryan made 10 more baskets than John. Matt made 2 times as many baskets as Ryan. All together, the boys made 86 baskets. How many baskets did each boy make?
x=14
Ryan: x + 10 = 24
John: x = 14
Matt: 2x + 20 = 48
500
2.5x + 1.5 - 4.6x = 18.3
x = -8
500
-3(-7 + 6m) > -42
m < 3.5
500
Does this graph show a direct proportion?
If yes, what is the constant?
How long does it take to drive 240 miles?
Yes
k = 60
It takes 4 hours to drive 240 miles.
500
Hailey paid $40.32 for 4.8 gallons of gas. Find the price of one gallon.
$8.40 per gallon
500
Stop & Shop is having a sale on soda. The price of one bottle of soda is $3.00. Stop & Shop is selling a sale pack of three bottles of soda for $7.50. Assuming you can afford (or want to) buy the three pack, how much money do you save per bottle by buying the sale pack versus individually?
You save $0.50 per bottle of soda.