Application Problems

Conversion or Ratio

1.) 1 inch = 2.54 centimeters

(a.) How many inches are there in 1 meter?

(b.) How many centimeters are in 1 yard?

2.) A lake that is 2½ miles wide appears to be ¼ of an inch wide on a map that is drawn to scale. How long is a road that appears to be 5/8 of an inch on the map?

3.) How many meters are in a mile if there are 2.54 centimeters in an inch, 12 inches in a foot, 5280 feet in a mile, and 100 centimeters in a meter?

Geometry

4.) How tall is a particular tree if it casts a 50 foot shadow at the same time that a six foot tall person casts a shadow that is 10 feet long?

5.) Find x if the area of the shaded region is 22 square units.

Problems involving percent

6.)  (a.) 5 is what % of 20?

(b.) What is 5% of 20?

(c.) 20 is 5% of what?

7.) Meijers buys a coat to sell in their store and marks it up 40% from their cost. Later they discount it 15% off the selling price. If the coat now costs $55, how much did it cost Meijers to purchase the coat?

Mixture Problems

8.) Given 2 feeds, feed A containing 45% crude protein and feed B containing 17% crude protein, how much of each should be used to yield a 1000 pound mixture containing 27% crude protein?

9.) Joe mixes a solution 8% acid. Sarah says that is too strong so she mixes in distilled water. How much water does Sarah need to add to 1 gallon of Joe’s solution to make the mixture 3% acid?

10.) A young couple decides to marry and combine their assets. For the past year she had $2000 in an account that pays 6% annual interest. He had $2500 in an account. What is the annual interest of his account if together they earned $250 in interest during the last year?

Rate × Time = Distance

11.) Jodi and Amy live 8 miles apart. They each decide to run to each other’s house. Jodi leaves 10 minutes before Amy. If Jodi runs 8 m.p.h. and Amy runs 9 m.p.h., how long from when Amy leaves until they meet?

12.) The cruising speed of an airplane is 200 m.p.h.. You want to go on a 4 hour round trip flying North as far as possible and turning around. How far North can you travel if there is a 30 m.p.h. wind blowing from the North?

Here’s a more realistic problem involving runners, the way runners really speak. In this case rate * time does not equal distance.:
13.) Brandon and Mark run in a 10 kilometer race. Brandon runs 6 min. per mile and Mark runs 6 min. 20 sec. per mile. How far will Mark have run when Brandon crosses the finish line? Note: There are 6.2 miles in 10 kilometers.

14.) After doing number 13, rework number 11 replacing Jodi’s speed with 7 min. per mile and Amy’s speed with 6 min. 30 sec. per mile.

Rate

15.) Suppose it takes Mat 12 hours to paint a house, and it would take Chrissy 15 hours to paint the same house. If they both work on it together painting at their same rates, how long will it take them to paint the house?

16.) Christine and Paul are hired to make the answer key for a Basic Algebra text. How long would it take Paul to do the job alone if together it takes them 20 hours and Christine could do the job alone in 35 hours?

Answers