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$$\frac{3}{a} - \frac{b}{14}$$ =$$\frac{1}{7}$$ and $$\frac{a}{15}=\frac{2}{b}$$ If a and b satisfy the equations above, what is the value of $$\frac{a}{b}$$?

Give your answer as a fraction. $$\frac{a}{b}$$=_________
An employee at a parcel delivery company weighs four boxes labeled $$A, B, C$$, and $$D$$. Box $$A$$ weighs $$\frac{1}{4}$$ kilogram and boxes $$B$$ and C each weigh $$\frac{5}{4}$$ kilograms. The ratio of the weight of box $$A$$ to the weight of box $$B$$ is the same as the ratio of the weight of box $$C$$ to the weight of box $$D$$. What is the weight of box $$D$$, in kilograms? Give your answer as a fraction. _________kilograms
The price of p pencils is d dollars. At this rate, what is the price of $$(p+2,000)$$ pencils, in dollars?
What is the greatest possible value of$$ ||x|-3|$$ for$$ -2 \leq x \leq 3$$?
Carlos owns twice as many books as Surya and one-third as many books as Ian. Ian owns 10 more books than Emma. Which of the following statements individually provide(s) sufficient additional information to determine how many books Carlos owns? Indicate all such statements.
$$x \gt 0$$ $$y$$ is $$25$$ percent greater than $$x$$. $$y^2$$ is p percent greater than $$x^2$$.

Quantity A

$$p$$

Quantity B

$$50$$


The manufacturing cost of a certain car model in 1995 was 10 percent greater than its manufacturing cost in 1990 and 10 percent less than its manufacturing cost in 2000.

Quantity A

The manufacturing cost of the car model in 2000 as a percent of its manufacturing cost in 1990

Quantity B

$$120%$$


The regular price of each item in a store was reduced by 15 percent during a special one-day sale. The day after the sale, the reduced price of each unsold item was replaced by its regular price. The regular price of each unsold item was what percent greater than its reduced price? Give your answer to the nearest whole percent. _________%
The rental on a certain beach house is $1,225 per week during the months of June, July, and August, and $110 per day during the rest of the year. Renting the house for 1 week during June, July, or August is what percent greater than renting the house for 1 week during the rest of the year?_________% Give your answer to the nearest whole percent.
Four friends had a meal at a restaurant, and the total cost of their meal was $$p$$ dollars. After adding a gratuity of 20 percent of the total cost of the meal, the friends divided the total amount, including gratuity, equally among themselves. If each of them paid $18.00, what is the value of $$p$$?_________
For each selling price greater than $300, a department store offers a discount equal to 10 percent of the first $300 and a discount equal to 15 percent of the amount of the selling price in excess of $300. What is the selling price for which the discount on the first $300 is the same as the discount on the amount in excess of $300?
Last year Juan planted a rectangular garden that was 20 feet long and 10 feet wide. This year he increased the length of the garden by 10 percent and the width by 20 percent. What was the percent increase in the area of Juan' s garden from last year to this year? _________%
The rate $$x$$ kilometers per hour is equal to the rate 10 centimeters per second.

Quantity A

$$xt$$

Quantity B

$$0.36$$


Quantity A

The time it takes Pat to drive 240 miles, driving at an average speed of 52 miles per hour

Quantity B

The time it takes George to drive 300 miles, driving at an average speed of 62 miles per hour


Antonia is driving a bus to City $$A$$. When she has driven half the total distance to the city, she notices that she has driven for 12 hours and averaged 35 miles per hour. She was scheduled for 19 hours driving time for the entire journey to City $$A$$. lf she is to arrive exactly on schedule, at what average speed, in miles per hour, must she drive the second half of the distance?
Cashews are valued at $10.00 per pound, and peanuts are valued at $4.00 per pound. At these rates, how many pounds of cashews would be needed to make 40 pounds of a mixture of cashews and peanuts that would be valued at $5.50 per pound?
$$0 \lt y \lt 1$$ 16y is an integer.

Quantity A

The tenths digit of y

Quantity B

$$2$$


A group of n people is standing in line to purchase theater tickets. The line is a straight line with more than 10 people. Meg is the 4th person behind the person at the front of the line, and Cory is the 4th person in front of the person at the back of the line.

Quantity A

The number of people in the line between Meg and Cory

Quantity B

$$ n-10$$


In the table above, if the sum of the numbers on each main diagonal is equal to the sum of the numbers in the four corners, what is the value of $$(p+q)-(x+y)$$?
$$n-r=8$$ and $$n^2-nr+r^2=78$$

Quantity A

$$nr$$

Quantity B

$$14$$


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