Proportional Relationships
A painter mixes 2 1/2 pints of yellow paint with 4 pints of red paint to make a certain shade of orange paint. How many pints of yellow paint should be mixed with 10 pints of red paint to make this shade of orange?
6.25 or 6 1/4 pints yellow paint
Simplify the following expression.
-6 + (-2d) + (-4d) + 3d
-6 + (-3d)
or
-6 - 3d
or
-3d - 6
What is 30% of 18?
5.4
Greg bought 19 and 11/16 gallons of gas. What decimal should the meter on the gas pump read?
19.6875
Solve for the given variable.
4y + 3 = 19
y=4
Sally is going on vacation with her family. In 2 hours they travel 90.5 miles. If they travel at the same speed, write an equation that represents how far they will travel, d, in h hours.
Expand the expression.
3.5(-3n + 4)
-10.5n + 14
or
14 - 10.5n
On Thursday, a restaurant serves iced tea to 35 of its 140 customers. What percent of the customers order iced tea?
25%
Find the sum.
64 + (-15)
49
Solve the equation -4(8 + y) = 90
-32 - 4y = 90
+32 +32
-4y = 122
y = -30.5
What are the two requirements that make a graph proportional?
straight line through the origin.
Simplify the expression.
(6x - 2y - 5) - (-5 + 9y - 8x)
14x - 11y
or
-11y + 14x
Sharon paid $78 sales tax on a new camera. If the sales tax rate is 6.5%, what was the cost of the camera?
$1,200
Penelope has a birdhouse that is 4 and 9/10 feet above the roof of her garage. She has a second birdhouse that is 5.36 feet below the roof of her garage. What is the distance between the birdhouses?
10.26 ft or
10 and 26/100 ft or
10 and 13/50 ft
Solve x - 19 > 81. Then graph the solution.
x > 100
Mealworms are a healthy food for wild songbirds. Adam buys a 3.5-oz container of mealworms for $8.75. Marco buys a 3.75-oz container of mealworms for $9.75. Which container is the better deal?
Hal earns n dollars per hour. Next month he will receive a 2% raise in pay per hour. The expression n + 0.02n is one way to represent Hal’s pay per hour after the raise. Write an equivalent simplified expression that will represent his pay per hour after the raise.
1.02n
Melissa estimated that she would read 250 pages last week. She read 290 pages. What is the percent error of Melissa’s estimate? Round to the nearest whole percent.
14%
Jason spends $2.35 to buy lunch at school. If he buys a lunch on 9 days, what number represents the total change in the amount of money Jason has?
-$21.15
Travis has 3 months to save money for a trip. An airplane ticket costs more than $300. If he saves the same amount of money, a, each month, how much does he need to save each month to pay for the ticket?
$100 or more each month
Does the table show a proportional relationship between x and y? If yes, what is the Constant of Proportionality?
x | y
200 | 600
400 | 1,200
500 | 1,500
Yes the table shows a proportional relationship. The COP is 3.
The area of a garden plot can be represented by the expression 84z - 54. The garden will be divided into six sections for planting six different vegetables. The sections will be equal in area. Write an expression that represents the area of each section.
14z - 9
Nya wants to buy a sweater that had an original price of $55. The sweater is now discounted 20% and the sales tax rate is 5.5%. How much will Nya pay for the sweater?
$46.42
-81 / -9
9
The school band gets $5 for each T-shirt they sell at a fundraiser. They have a goal of raising $150. If $45 has been raised so far, write and solve an inequality for how many more T-shirts, t, do they have to sell to reach or exceed the goal?
45 + 5t >= 150
t >= 21