# 5.4 Solve applications with systems of equations  (Page 9/11)

 Page 9 / 11

Two angles are complementary. The measure of the larger angle is ten more than four times the measure of the smaller angle. Find the measures of both angles.

Wayne is hanging a string of lights 45 feet long around the three sides of his rectangular patio, which is adjacent to his house. The length of his patio, the side along the house, is five feet longer than twice its width. Find the length and width of the patio.

The width is 10 feet and the length is 25 feet.

Darrin is hanging 200 feet of Christmas garland on the three sides of fencing that enclose his rectangular front yard. The length is five feet less than five times the width. Find the length and width of the fencing.

A frame around a rectangular family portrait has a perimeter of 60 inches. The length is fifteen less than twice the width. Find the length and width of the frame.

The width is 15 feet and the length is 15 feet.

The perimeter of a rectangular toddler play area is 100 feet. The length is ten more than three times the width. Find the length and width of the play area.

Solve Uniform Motion Applications In the following exercises, translate to a system of equations and solve.

Sarah left Minneapolis heading east on the interstate at a speed of 60 mph. Her sister followed her on the same route, leaving two hours later and driving at a rate of 70 mph. How long will it take for Sarah’s sister to catch up to Sarah?

It took Sarah’s sister 12 hours.

College roommates John and David were driving home to the same town for the holidays. John drove 55 mph, and David, who left an hour later, drove 60 mph. How long will it take for David to catch up to John?

At the end of spring break, Lucy left the beach and drove back towards home, driving at a rate of 40 mph. Lucy’s friend left the beach for home 30 minutes (half an hour) later, and drove 50 mph. How long did it take Lucy’s friend to catch up to Lucy?

It took Lucy’s friend 2 hours.

Felecia left her home to visit her daughter driving 45 mph. Her husband waited for the dog sitter to arrive and left home twenty minutes (1/3 hour) later. He drove 55 mph to catch up to Felecia. How long before he reaches her?

The Jones family took a 12 mile canoe ride down the Indian River in two hours. After lunch, the return trip back up the river took three hours. Find the rate of the canoe in still water and the rate of the current.

The canoe rate is 5 mph and the current rate is 1 mph.

A motor boat travels 60 miles down a river in three hours but takes five hours to return upstream. Find the rate of the boat in still water and the rate of the current.

A motor boat traveled 18 miles down a river in two hours but going back upstream, it took 4.5 hours due to the current. Find the rate of the motor boat in still water and the rate of the current. (Round to the nearest hundredth.).

The boat rate is 18 mph and the current rate is 2 mph.

A river cruise boat sailed 80 miles down the Mississippi River for four hours. It took five hours to return. Find the rate of the cruise boat in still water and the rate of the current. (Round to the nearest hundredth.).

A small jet can fly 1,072 miles in 4 hours with a tailwind but only 848 miles in 4 hours into a headwind. Find the speed of the jet in still air and the speed of the wind.

The jet rate is 240 mph and the wind speed is 28 mph.

A small jet can fly 1,435 miles in 5 hours with a tailwind but only 1215 miles in 5 hours into a headwind. Find the speed of the jet in still air and the speed of the wind.

A commercial jet can fly 868 miles in 2 hours with a tailwind but only 792 miles in 2 hours into a headwind. Find the speed of the jet in still air and the speed of the wind.

The jet rate is 415 mph and the wind speed is 19 mph.

A commercial jet can fly 1,320 miles in 3 hours with a tailwind but only 1,170 miles in 3 hours into a headwind. Find the speed of the jet in still air and the speed of the wind.

## Everyday math

At a school concert, 425 tickets were sold. Student tickets cost $5 each and adult tickets cost$8 each. The total receipts for the concert were $2,851. Solve the system $\left\{\begin{array}{c}s+a=425\hfill \\ 5s+8a=2,851\hfill \end{array}$ to find $s$ , the number of student tickets and $a$ , the number of adult tickets. $s=183,a=242$ The first graders at one school went on a field trip to the zoo. The total number of children and adults who went on the field trip was 115. The number of adults was $\frac{1}{4}$ the number of children. Solve the system $\left\{\begin{array}{c}c+a=115\hfill \\ a=\frac{1}{4}c\hfill \end{array}$ to find $c$ , the number of children and $a$ , the number of adults. ## Writing exercises Write an application problem similar to [link] using the ages of two of your friends or family members. Then translate to a system of equations and solve it. Answers will vary. Write a uniform motion problem similar to [link] that relates to where you live with your friends or family members. Then translate to a system of equations and solve it. ## Self check After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section. On a scale of 1-10, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this? #### Questions & Answers -65r to the 4th power-50r cubed-15r squared+8r+23 ÷ 5r WENDY Reply write in this form a/b answer should be in the simplest form 5% August Reply convert to decimal 9/11 August Equation in the form of a pending point y+2=1/6(×-4) Jose Reply write in simplest form 3 4/2 August definition of quadratic formula Ahmed Reply From Google: The quadratic formula, , is used in algebra to solve quadratic equations (polynomial equations of the second degree). The general form of a quadratic equation is , where x represents a variable, and a, b, and c are constants, with . A quadratic equation has two solutions, called roots. Melissa what is the answer of w-2.6=7.55 What Reply 10.15 Michael w = 10.15 You add 2.6 to both sides and then solve for w (-2.6 zeros out on the left and leaves you with w= 7.55 + 2.6) Korin Nataly is considering two job offers. The first job would pay her$83,000 per year. The second would pay her $66,500 plus 15% of her total sales. What would her total sales need to be for her salary on the second offer be higher than the first? Mckenzie Reply x >$110,000
bruce
greater than $110,000 Michael Estelle is making 30 pounds of fruit salad from strawberries and blueberries. Strawberries cost$1.80 per pound, and blueberries cost $4.50 per pound. If Estelle wants the fruit salad to cost her$2.52 per pound, how many pounds of each berry should she use?
$1.38 worth of strawberries +$1.14 worth of blueberries which= $2.52 Leitha how Zaione is it right😊 Leitha lol maybe Robinson 8 pound of blueberries and 22 pounds of strawberries Melissa 8 pounds x 4.5 = 36 22 pounds x 1.80 = 39.60 36 + 39.60 = 75.60 75.60 / 30 = average 2.52 per pound Melissa 8 pounds x 4.5 equal 36 22 pounds x 1.80 equal 39.60 36 + 39.60 equal 75.60 75.60 / 30 equal average 2.52 per pound Melissa hmmmm...... ? Robinson 8 pounds x 4.5 = 36 22 pounds x 1.80 = 39.60 36 + 39.60 = 75.60 75.60 / 30 = average 2.52 per pound Melissa The question asks how many pounds of each in order for her to have an average cost of$2.52. She needs 30 lb in all so 30 pounds times $2.52 equals$75.60. that's how much money she is spending on the fruit. That means she would need 8 pounds of blueberries and 22 lbs of strawberries to equal 75.60
Melissa
good
Robinson
👍
Leitha
thanks Melissa.
Leitha
nawal let's do another😊
Leitha
we can't use emojis...I see now
Leitha
Sorry for the multi post. My phone glitches.
Melissa
Vina has $4.70 in quarters, dimes and nickels in her purse. She has eight more dimes than quarters and six more nickels than quarters. How many of each coin does she have? Mckenzie Reply 10 quarters 16 dimes 12 nickels Leitha A private jet can fly 1,210 miles against a 25 mph headwind in the same amount of time it can fly 1,694 miles with a 25 mph tailwind. Find the speed of the jet. Crispy Reply wtf. is a tail wind or headwind? Robert 48 miles per hour with headwind and 68 miles per hour with tailwind Leitha average speed is 58 mph Leitha Into the wind (headwind), 125 mph; with wind (tailwind), 175 mph. Use time (t) = distance (d) ÷ rate (r). since t is equal both problems, then 1210/(x-25) = 1694/(×+25). solve for x gives x=150. bruce the jet will fly 9.68 hours to cover either distance bruce Riley is planning to plant a lawn in his yard. He will need 9 pounds of grass seed. He wants to mix Bermuda seed that costs$4.80 per pound with Fescue seed that costs $3.50 per pound. How much of each seed should he buy so that the overall cost will be$4.02 per pound?
33.336
Robinson
Amber wants to put tiles on the backsplash of her kitchen counters. She will need 36 square feet of tiles. She will use basic tiles that cost $8 per square foot and decorator tiles that cost$20 per square foot. How many square feet of each tile should she use so that the overall cost of the backsplash will be $10 per square foot? Imaan Reply Ivan has$8.75 in nickels and quarters in his desk drawer. The number of nickels is twice the number of quarters. How many coins of each type does he have?
2q=n ((2q).05) + ((q).25) = 8.75 .1q + .25q = 8.75 .35q = 8.75 q = 25 quarters 2(q) 2 (25) = 50 nickles Answer check 25 x .25 = 6.25 50 x .05 = 2.50 6.25 + 2.50 = 8.75
Melissa
John has $175 in$5 and $10 bills in his drawer. The number of$5 bills is three times the number of $10 bills. How many of each are in the drawer? mikayla Reply 7-$10 21-$5 Robert Enrique borrowed$23,500 to buy a car. He pays his uncle 2% interest on the $4,500 he borrowed from him, and he pays the bank 11.5% interest on the rest. What average interest rate does he pay on the total$23,500? (Round your answer to the nearest tenth of a percent.)
Two sisters like to compete on their bike rides. Tamara can go 4 mph faster than her sister, Samantha. If it takes Samantha 1 hour longer than Tamara to go 80 miles, how fast can Samantha ride her bike?
8mph
michele
16mph
Robert
3.8 mph
Ped
16 goes into 80 5times while 20 goes into 80 4times and is 4mph faster
Robert
help me understand graphs