QR20 PS 41 to 50

As shown in the diagram above, a lever resting on a fulcrum has weights of w₁ pounds and w₂ pounds, located d₁ feet and d₂ feet from the fulcrum. The lever is balanced and w₁d₁=w₂d₂. Suppose w₁ is 50 pounds and w₂ is 30 pounds. If d₁ is 4 feet less than d₂, what is d₂, in feet?

PS14237

If r and s are positive integers such that (2^r)(4^s) = 16, then 2r + s =

PS01650

Three people each contributed x dollars toward the purchase of a car. They then bought the car for y dollars, an amount less than the total number of dollars contributed. If the excess amount is to be refunded to the three people in equal amounts, each person should receive a refund of how many dollars?

PS06726

Last week Jack worked 70 hours and earned $ 1,260. If he earned his regular hourly wage for the first 40 hours worked, 3/2 times his regular hourly wage for the next 20 hours worked, and 2 times his regular hourly wage for the remaining 10 hours worked, what was his regular hourly wage?

PS07080

If a and b are positive integers and (2^a)^b = 2³, what is the value of 2^a*2^b?

PS13426

Five machines at a certain factory operate at the same constant rate. If four of these machines, operating simultaneously, take 30 hours to fill a certain production order, how many fewer hours does it take all five machines, operating simultaneously, to fill the same production order?

PS01099

A certain toll station on a highway has 7 tollbooths, and each tollbooth collects $0.75 from each vehicle that passes it. From 6 o’clock yesterday morning to 12 o’clock midnight, vehicles passed each of the tollbooths at the average rate of 4 vehicles per minute. Approximately how much money did the toll station collect during that time period?

PS01443

How many integers between 1 and 16, inclusive, have exactly 3 different positive integer factors? (Note: 6 is NOT such an integer because 6 has 4 different positive integer factors: 1, 2, 3, and 6.)

PS13829

Stephanie has 9/4 cups of milk on hand and makes 2 batches of cookies, using 2/3 cup of milk for each batch of cookies. Which of the following describes the amount of milk remaining after she makes the cookies?

PS14063

The expression n! is defined as the product of the integers from 1 through n. If p is the product of the integers from 100 through 299 and q is the product of the integers from 200 through 299, which of the following is equal to p/q?

PS01656