Linear Equations Application Exercises Accelerated Math 1010/ 1050

How to Begin: 1. Read the question. 2. Identify type of problem. 3. Set up approach to solving & write equations. (Draw a picture to help.) 4. Do the math. What are you trying to solve for? 5. Read the final question; does the answer make sense in the context of the problem? (i.e. distance is never negative)

Distance Word CluesMethod 0 Distance: 0 Miles, kilometers 0 Rate: 0 miles per hour, 0 Time: 0 minutes, seconds, hours D=rt Person/ Vehicle A Person/ Vehicle B

Geometry Word CluesMethod 0 Shapes: 0 Rectangular 0 Triangular 0 Circular 0 Trapezoid 0 Cylinder 0 Box

Mixture Problems Word CluesMethod 0 Percentages of measurements in weight, volume, capacity 0 mixture 0 Solutions, nuts, coffee, candies Amount%Total Item Type A Item Type B Mixture

Simple Interest Word CluesMethod 0 Interest, rate 0 Principle invested in dollars 0 Amount of money 0 Time in years IPrt Account A Account B Total Amount =

Work –Ratio Problems Word CluesMethod 0 Amount of activity performed in unit of time 0 two or more participants 0 Question of ratio to complete job “together”

Other Types 0 Given formula(s) → Plug it in. 0 The sum or difference of two or more numbers → See translation table handout. translation table handout 0 Interpretation → Know your terminology.

Question #1 0 A car leaves Salt Lake City traveling at 70mph. An hour later, a second car leaves Salt Lake City following the first car, speeding at 80 mph. How many hours after leaving Salt Lake City will it take the second car to catch up to (pass, overtake) the first car? 0 HINT: Both cars leave Salt Lake. When the 2 nd car catches up to, passes, or overtakes the 1 st car, we understand that they have traveled the same distance.

Solution #1 Drt Car 170mph Car 280mph

Question #2

Solution #2 Drt Plane 1D520mph Plane D Total3000

Question #3 0 Marie rode her bike from her house to her brother Donny’s house, averaging 20mph. Later Donny drove her home in his car at 30mph. If Marie’s total travel time was 3 hours, how far away does she live from Donny? 0 HINT: We understand that the distance in each direction is equal.

Solution #3 Drt BikeD20mph CarD30mph 3

Question #4 0 If a hole is 4 feet in diameter, how deep must the hole be in order to hold 113 cubic feet of dirt. Round to the nearest whole foot. 0 HINT: How do you measure the volume of a cylinder?

Solution #4

Question #5 0 The width of a rectangle is 3 less than one-half its length, and the perimeter of the rectangle is 51 feet. Find its dimensions. 0 HINT: This is a geometry problem that requires careful word translation. See English to Math Translation handout.English to Math Translation handout

Solution #5

Question #6 0 The perimeter of a rectangle is 38 inches. The width of a rectangle is 1 inch more than half its length. What is the area of the rectangle?

Solution #6

Question #7 0 A trapezoid has an area of 35 square centimeters. Assuming that one base is 9 centimeters and the other base is 11 centimeters, find the height of the trapezoid. 0 HINT: What is the formula for the area of a trapezoid?

Solution #7

Formula for a Trapezoid

Question #8 0 You need a 15% acid solution for a certain test, but you only have a 10% solution and a 30% solution. You need 10 liters of the 15% acid solution. How many liters of 10% solution and 30% solution should you use?

Solution #8 1. Read the question. 0 need a 15% acid solution 0 have a 10% solution and a 30% solution 0 need 10 liters of the 15% acid solution 0 How many liters of 10% solution (A) and 30% solution (B) should you use? 2. Identify type of problem. 0 Mixture 3. Set up approach to solving. (Draw a picture to help.) 0 In this case we have 2 unknowns so will need to equations. Amount of Solution % of AcidNeeded Solution A Solution B Mixture

Solution #8 con’t

Question #9 0 Find the selling price per pound of a coffee mixture made from 8 pounds of coffee that sells for $9.20 per pound and 12 pounds of coffee that costs $5.50 per pound. Answer: $6.98/lb

Solution #9 Weight in lbs.Price per lb.Total Cost Coffee 18lbs$9.20/lb Coffee 212lbs$5.50/lb Coffee Mixture 20lbs

Question #10 Answer: 70% alcohol solution = 25 liters

Solution #10 # of liters% of alcoholTotal 70% solution.7 40% solution50.4.4(50) Mixture.5

Question #11

Solution #11

Question #12 0 Helen Weller invested $14,000 in an account that pays 10% simple interest. How much additional money must be invested in an account that pays 13% simple interest so that the average return on the two investments amounts to 11%?

Solution #12 PrtI Account 1$14,000 10%1 Account 2 13%1 Both Accounts 11%1 =.11($14,000+x)

Question #13

Solution #13

Question #14 0 Mr. Holland invested $4900, part at 6% interest and the rest at 8%. If the yearly interest on each investment is the same, how much interest does he receive at the end of the year? 0 HINT: The yearly interest on each investment is the same for each amount invested. This means we can solve for I and set the two equal to each other.

Solution #14 IPrtTotal Account 1P6% 1 Account 2$4900-P8% 1 Total Amount $4900

Question #15 0 President Obama can mow the White House lawn in 4 hours on his tractor mower. President Clinton mowed the lawn in 5 hours on his. How long would it take them to mow the lawn together. 0 HINT: Obama does ¼ of the job in one hour and Clinton does 1/5 of the job in one hour. How much of the job could they do together in one hour?

Solution #15

Question #16