Algebra Word Problems - KET

1 WORKPLACE LINK: Nancy works at a clothing store. A customerwants to know the original price of a pair of slacks that are now on salefor 40% off. The sale price is $ Nancy knows that 40% of the originalprice subtracted from the original price will equal the sale price. Using xfor the original price she writes: x Then she solves for Word ProblemsMany Algebra Problems are about number relationships. In most word Problems , one number is defined by describing its relationship to another number. One other fact, such as the sum orproduct of the numbers, is also given. To solve the problem , you need to find a way to expressboth numbers using the same how to write an equation about two amounts using one : Together, Victor and Tami Vargas earn $33,280 per year. Tami earns $4,160 more peryear than Victor earns. How much do Victor and Tami each earn per year?You are asked to find two unknown amounts. Victor s earnings: xRepresent the amounts using s earnings: x+4,160 Write an equation showing that the sum of thetwo amounts is $33,280.

2 Solve the +x+4,160=33,280 Combine like +4,160=33,280 Subtract 4,160 from both sides of the +4,160 4,160=33,280 4,1602x=29,120 Divide both sides by ,560 Now go back to the beginning, when you first wrote the amounts in algebraic language. Since xrepresents Victor s earnings, you know that Victor earns $14,560 per year. Tami s earnings arerepresented by x+4,160. Add: 14,560 +4,160 =18,720. Tami earns $18,720 per : Victor earns $14,560,and Tami earns $18, : Return to the original word problem and see whether these amounts satisfy the conditionsof the problem . The sum of the amounts is $33,280, and $18,720 is $4,160 more than $14, answer is how to apply algebraic thinking to Problems about :Erica is four times as old as Blair. Nicole is three years older than Erica. The sum of their ages is 21. How old is Erica?The problem concerns three ages. Let xequal Blair s age. Blair s age: xRepresent the amounts using the same s age: 4xNicole s age: 4x+3 Write an equation showing the sum equal to +4x+4x+3 = 21262 MATHEMATICS882x229, two numbers if one number is 3 morethan twice another, and their sum is is 8 years less than twice Paula s sum of their ages is 40.

3 How old is Erin? and Roy do landscaping. They recentlyearned $840 for a project. If Lyle earned $4 for every $1 earned by Roy, how much of the money went to Lyle? sum of four consecutive numbers is the four movie theater sold 5 times as manychildren s tickets as adult tickets to anafternoon show. If 132 tickets were sold inall, how many were children s tickets? , Grace and Carlo spent $51 on agift. If Grace contributed twice as muchmoney as Carlo, how much did Carlo spend? s age is of Mia s age. The sum of their ages is 91. How much older isMia than Fahi? sum of two consecutive odd numbersis 64. Name the numbers. (Hint:Let xrepresent the first number and x+2 thesecond number.) number is 8 more than of anothernumber. The sum of the numbers is 23. What are the numbers? , Julius, and Tia volunteered toread to children at the public worked two hours less than worked twice as many hours asJulius. Altogether they worked 58 many hours did Adena work?

4 (1)14(4)42(2)16(5)46(3)28 Answers and explanations start on page the + 4x+ 4x+ 3=21 The variable xis equal to 2, but that 9x+ 3=21doesn t answer the question posed in the9x=18problem. The problem asks you to findErica s age, which is equal to 4x, or 4(2).x=2 Answer:Erica is 8 years :Blair is 2, Erica is 8, and Nicole is 11. The ages total how to write equations for consecutive number :The sum of three consecutive numbers is 75. Name the numbersare numbers in counting order. To solve Problems of this type, let xequalthe first number. The second and third numbers can be expressed as x+ 1 and x+ an + x+ 1 + x+ 2=75 + 3=75 3x=72 x=24 Answer:The numbers are 24, 25, and : The numbers are consecutive, and their sum is K I L L P R A C T I C EFor each problem , write an equation and solve. Check your 38:Introduction to AlgebraThis workedexample does notshow every step. Asyou gain experience,you will do many ofthe steps LINK: For a grant application, Jodi is sketching theproposed landscaping plan for a new community center.

5 The plan calls fora rectangular garden. Jodi needs the dimensions of the rectangle to drawthe plan. She knows that the length is two times the width and that theperimeter is 126 meters. Jodi writes an equation to find the Algebra Word ProblemsMany Algebra Problems are about the figures that you encounter in geometry. To solve theseproblems, you will need to combine your understanding of geometry and its formulas with yourability to write and solve how to solve for the dimensions of a : In the situation above, Jodi is given the perimeter of a rectangle. She also knows that the length is twice as many meters as the width. Using the formula for finding the perimeterof a rectangle, find the dimensions of the formula for finding the perimeter of a rectangle is P =2l+2w, where l=length and w=width. You will be given a page of formulas when you take the GED Math Test. A copy of that page is printed for your study on page 340 of this book.

6 When an item on the GED Math Test describes a figure in words alone, your first step should be to make a quick sketch of the figure. Read the problem carefully, and label your sketch with the information you have been this case, let xrepresent the width and 2xthe substitute the information you have into the formula and +2w126=2(2x) +2(x)126=4x+2x126=6x21=xAnswer: The rectangular garden is 21 meters wideand 42 meters long. Check:Make sure the dimensions meet the condition of the problem . Substitute the dimensionsinto the perimeter formula: P =2(21) +2(42) = 42 + 84 =126 meters. The answer is common type of Algebra problem involves the denominations of coins and bills. In thistype of problem , you are told how many coins or bills there are in all. You are also given thedenominations of the coins or bills used and the total amount of money. Your task is to find howmany there are of each = 126 m2xx8If the width (x) is 21 meters, thenthe length (2x) must be 42 length of a rectangle is 4 inchesmore than twice its width.

7 If theperimeter of the rectangle is 38 inches,what is its width? perimeter of a right triangle is 60 A is 2 cm less than half of Side C is 2 cm longer than Side B. Find the lengths of the three bag contains a total of 200 quartersand dimes. If the total value of the bag scontents is $ , how many quartersand how many dimes are in the bag? school sold 300 tickets to a basketballgame. Tickets were $9 for adults and $5 forchildren. If the total revenue was $2340,how many of each ticket type were sold?Learn how to solve denomination Problems by studying this : Marisa is taking a cash deposit to the bank. She has $10 bills and $5 bills in a depositpouch. Altogether, she has 130 bills with a total value of $890. How many bills of each kind arein the pouch?Let xrepresent the number of $10 bills in the bag. Next, use the same variable to represent thenumber of $5 bills. If there are 130 bills in all, then 130 xrepresents the number of $5 you need to establish a relationship between the number of bills and their value.

8 Using the expression above, the total value of the $10 bills is 10x, and the total value of the $5 bills is 5(130 x).Write an equation and solve. 10x + 5(130 x)=890 Multiply both terms in parentheses by + 650 5x=890 Combine like + 650=890 Subtract 650 from both both sides by 5 to get the x=48number of $10 x=82 Subtract to find the number of $5 : There are 48 ten-dollar billsand82 five-dollar bills. Check:(48 $10) + (82 $5) = $480 + $410 = $890. The answer is K I L L P R A C T I C ESolve each 38:Introduction to Algebra8 Seeing a pattern can help you solve Algebra Problems . Suppose you were asked to find the sum of the whole numbers from 1 to 100. What would you do?In 1787, ten-year-old Carl Gauss was given this problem . As the other students began adding on theirslates, Carl solved the problem mentally. Carl observed that by adding the highest and lowest numbers in the sequence and working toward the middle he could find pairs that equaled 101: 1 +100 = 101, 2 +99 = 101, 3 +98 = 101, and so on.

9 Carl knew there must be 50 pairings in all. He multiplied 101 by 50 and got 5050, the correct sum. Carl Gauss went on to become a famous Carl s method here. Find the sum of the even whole numbers from 2 to and explanations start on page I S T O RYC o n n e c t i o n329 ANSWER KEYS kill Practice, page 2551. 322. 183. 604. 245. 46. 257. is equivalent to adding , or inside the parentheses first: 6( 5) = the exponent, then add inside theparentheses:=== Solver Connection, page 2556 4 +2 3 =1or 6 +( 4) +2 +( 3) =1 Skill Practice, page 2571. 9a 3b 42. 7x 33. 3x+424. 2m2 2m+125. 13a2 3b +2yDo the division and multiplicationfirst: =2yand 2(x 2y) =2x 4y. Thensimplify by combining all like 228. 1089. 410. 4811. 7012. 4213. 414. 815. 2 First find the numerator: 2x2+y=2(9)+2=20. Then find the denominator: 5x ( 5) =5( 3)+5 = 10. Divide: = ,000 Instead of computing fractions of p, you can start by combining terms: 4p+ + 6p.

10 Substitute andsolve: 100 6p= 100 6 20 = 12, Practice, page 2591. (Note: x1=x)8. 1029. 10 3In standard form, 10 3= and 10 2= 105In standard form, 105=360,000 and 104= 94,000. 15. 105sq mi16. 3,614,000 sq ,000,000,000,000 miles This number isread 25 trillion. timesSince our place value system isbased on tens, a difference of 1 in the exponentchanges the number by a factor of 10. 19. 2 10 3 Skill Practice, page 7=12y=8y= 2+14=19=5 10=5x 2= 15n 4= 95n= 5n= 4b+18=2b18=6b3= 5=0=5a= 4x+=368x+x=729x=72x=87. 3x+6=423x=36x=128. 5x 9= 145x= 5x= 19.+5=1= 432= 4x 8=x10. 2x 22=42x=26x=13 Skill Practice, page numbers are 18 and 39. first number =x, second number =2x+3x+2x+3=573x+3=573x=54x= is s age =x, Erin s age =2x 82x 8 +x=403x 8=403x=48x=16( 4)242(82+ 20)11(64+ 20)1144114y220 10a6 10x earned $ s earnings =x, Lyle s earnings =4x4x+x=8405x=840x= , 156, 157, and 158x+x+1 +x+2 +x+3 =6264x+6 =6264x=620x= tickets =x, children s tickets =5xx+5x=1326x=132x=226.