Word Problems (35 problems)

When a number is increased by 33 the result is 17. Find the number.

Train A leaves a station traveling at 48 miles per hour. Four hours later, train B leaves the same station traveling in the same direction at 58 miles per hour. How long will it take train B to catch train A?

We have two large bottles, one with pure antifreeze and the other with 40% antifreeze. How much we need to combine from each bottle so get 20 quarts of 50% antifreeze.

One-half of the boys and one-third of the girls of Mathematica High attended the homecoming game, whereas one-third of the boys and one-half of the girls attended the homecoming dance. If there were 570 students at the game and 580 at the dance, then how many students are there at Mathematica High?

Find two numbers such that their sum is 31 and one of then is four more than twice the other.

Area of a sail, a triangular sail has an area of x² + 5x + 6 square meters and a height of x + 3 meters. Find the length of the sail’s base.

A home-based company produces both hand-knitted scarves and sweaters. The scarves take 2 hours of labor to produce, and the sweaters take 14 hours. The labor available is limited to 40 hours per week, and the total production capacity is 5 items per week. Write a system of inequalities representing this situation, where x is the number of scarves and y is the number of sweaters. Then graph the system of inequalities.

The width of a rectangle is 29cm. Find all possible values for the length of the rectangle if the perimeter is a least 752cm.

The perimeter of a rectangle is to be no greater than 300 in., and the length must be 125 in. Find the maximum width of the rectangle.

Avoiding a collision, a car is traveling on a road that is perpendicular to a railroad track. When the car is 30 meters from the crossing, the car’s new collision detector warns the driver that there is a train 50 meters from the car heading toward the same crossing. How far is the train from the crossing?

The total height of a building and the flagpole on the roof is 230 feet. The building is 9 times as high as the flagpole. How high is the flagpole?

Venture capital, Henry invested $12,000 in a new restaurant. When the restaurant was sold two years later, he received $27,000. Find his average annual return by solving the equation 12,000 (1 + r) ² = 27,000

The length of a rectangular playground is 8 yards more than three times its width. If the perimeter of the playground is 208 yards, what are its dimensions?

A corporation allows each of its traveling employees a daily meal allowance and a nightly hotel allowance. One employee travels 4 days and 4 nights and is allotted $480. Another employee travels for 3 days and 2 nights and is allotted $270. What is the daily meal allowance and the nightly hotel allowance?

Winter wheat, while finding the amount of seed needed to plant his three square wheat fields. Hank observed that the side of one field was 1 kilometer longer than the size of the smallest field and that the side of the largest field was 3 kilometers longer than the side of the smallest field. If the total area of the three is 38 square kilometers, then what is the area of each field?

You pay $112 total for 2 tires, each of which are on sale for 30% off. After the sale is over you realize you need two more tires. How much will each of the two tires cost at the regular price?

Find all the numbers such that the number plus 3 times its inverse equals 4.

Anna has 12 bills in her wallet, some $5 and some $10. The total value of the bills is $100. How many of each bill does Anna have?

In Michigan, speeding fines are determined by the formula: F = 10(x – 65) + 50 were

F is the cost, in dollars, of the fine if a person is caught driving x miles per hour. If the fine comes to $400, how fast was that person speeding?

A company budgets $30,000 for advertisement costs promoting a new product. Television ads cost 500 dollars each and radio ads cost 100 dollars each. If the company wants to buy a total of 220 ads, how many television ads and radio ads should the company buy?