G.SRT.2 Worksheet 1 Guide what is a proportion? <(i^t, | y^cr-{ios (Ar*+'*t\ e6po\ How do we determine if two ratios are equat? U6e- AC ,=- IJJ Zir Lf-tz cyo75*p rod u c.{s J(t.) 3 Y&) 7o {>a How do we solve a proportion? 6&".a) =3* b)r.-se = =r 2 sx = 0('s) 5X: ?b *7a=-7Y We can use proportions and ratios to solve lots of different problems. Here are a few examples. 1. The ratio of boys to girs in the class is 4:3. lf there are 20 boys in the class, how many girls are there? 2. The ratio of boys to girls in the class is bogs 1:3. lf there are 28 students in the clas, how many girls are there? gvtc ,r+ tx' -2ff *x=L& 3. A triangte has angles in , ,rtifloirl,s, *t tx + zy +)x = ltro tr-a x:7 " 6 /' =- at is the size of each angle? /(t.) = F-"-1\ p{zo\ = leo I TLer\ *, r}{ h + t'^r"^i\' lZ:J 4. What are the possible names for the quadrilateralwith sides 3:1:3:1? 3Y lyJ---ltx L-' 9)r 5. A recipe instructs the cook to use 4 cups of water for each 3 cups of powder. lf you used 10 cups of water, how much powder should be added? ttso*ttr -t q y ".-' i 4Y =7o X X=1'S- 5. The soccer club has 3:2 of iuniors to freshman. lf the club how many juniors are there? 3@ 3x has 45 students attend #<shYw,.,* Jor't'rsr,J + 7y = Vr 5X=?r that are fresh4gqenlu J (?) zu) = tt Fr<Sh.*av- X-1 7. The sides of a triangle are in the ratio of 3:8:7. lf the perimeter of the triangle side? 3Y + 6x +'1P = e 7 ItrtL -* b3 Y=7'{ is 63 cm, how l.s-) = /l.r) = Lo"yuJ- 2t e* j,l. f c,r^ rrt; dtt- NAME: G.SRT.z WORKSHEET #7 1. Solve each proportion using cross products' a) 3x 1 515 x= e) c) b) x+l x d) 20*x 6 x4 x+15 4 x+2 t2 2x+13 -=-x= X= f) s) x-L 9 4 =-x-7 x= h) x-9 2 x 5 x4 -=s16 x= 2. Sotve the following problems. (Show work) t5 foot building casts a 9 foot shadow. How tall building that casts a 30 ft shadow at the same time? a) The ratio of seniors to juniors in the Chess Club is 2:3' there are 24 juniors, how many seniors are in the club? b) A c) A picture is 3 in. wide by 5 in. high was enlarged so that the width was 15 inches. How high is the enlarged d) Cameron picture? e) A triangle's three angles are in the ratio of is the measure of the smallest angle? 5:7:8' What is the has been eating 2 dollar menu burgers every week (7 days). At that rate, how many hamburgers will he in 4 weeks? f) A 5 foot high school boy casts a shadow of 24 inches. At the same time of day a girl at the elementary school park casts a shadow of 14 inches.' How tall is she (in feet)? G.SRT.2WORKSHEEI #7 that has the following ratios for its slDES. 3. what would be the best (most specific) name for the shape a)3:4:3 b)4: c)3:3:5:5 d) 5 :4: 5 G'G,G,G or-or that has the following ratios for its ANGLES' 4. what would be the best (most specific) name for the shape a)3:4:3 b)4: cl2:2:7:7 dl 5 :4: 5 or- 4:4:4:4 5. Solve the following problems. (Show work) a) The ratio of two supplementary angles is measures of each 4:5. Find the angle. the on AD? e) points A, B, c, and D are placed in alphabetical order a line so that AB = 2BC =CD. What is the ratio BD : two number? g) Two numbers are in ratio 7 : 3. The sum of the numbers is 36. what is the largest 2:3' Find the measures of each angle' two pieces. The ratio of two pieces is 5:7. How big are the two pieces? c) A 3 foot stick is broken into b) The ratio of two complementary angles is d) ls the largest angle acute, right or obtuse in that has angles measures in ratio, 2:3:4? a triangle f) Points A, B, and C are placed in alphabetical order on a line so that 3AB : AC. What is the ratio of AB : BC? h) Three numbers are in the ratio of 2 : 5 : 3. lf the largest number is 65. what is the smallest number? NAME, U G.SRT.2 WORKSHEET #7 1. Solve each proportion using cross products' b) a) 3x s t6 -=x x+15 15 gy= ttf Y-1 x+l _ c) d) 20-x 6 4 x+2 12 x4 2x+13 by = tb-qY /o )< =to -x= x= f) h) x-t 39x-92x4 -:- -:4x-7x5516 6x -=- l(-+K = bx'b lY'-q;=zv 1x = 4f 4L -rx+t" =o '(x-t\Lx-+\ --o ffii--1 *= lx=1lz- I v-'-tf L__ 2. Solve the following problems. (Show work) a) The ratio of seniors to juniors in the Chess Club is 2:3' there are 24 juniors, how many seniors are in the club? t5 foot building casts a 9 foot shadow. How tall building that casts a 30 ft shadow at the same time? b) A is the P L-.13 -2v 3X = tl( K= tb 6 Sux,w c)A picture is 3 in. wide by 5 in. high was enlarged the width was 15 inches' How high is the enlarged so picture? has been eating 2 dollar menu burgers every week (7 days). At that rate, how many hamburgers will he d) Cameron in 4 weeks? 3t{ t- -:--r- x Jtr='If x'- L{ e) A triangle's three angles are in the ratio of is 5:7:8' What the measure of the smallest angle? tx + lx + tx =- lro e@X = L{o {=1 { (q) f) A 6 foot high school boy casts a shadow of 24 inches' At the same time of day a girl at the elementary school park casts a shadow of 14 inches. How tall is she (in feet)? 2 G.SRT.z WORKSHEET #7 ratios for its SlDEs. 3. What would be the best (most specific) name for the shape that has the following 1qo56.e,le2 a)3:4:3 anr-i\ b) 4 : 5 : 4 : d) c)3:3:5:5 5 Pa".r,t\r,\03,*r^o1 P'sa$"'^fL'- .6'.6,G'.6 or ratios for its ANGLES. 4. What would be the best (most specific) name for the shape that has the following b)4: a)3:4:3 cl2:2 :7 :7 l4gcele-t Tra-Pzznif, 5 :4: dl 4 : 4 : 4 : 5 oY StUo^",*4 F,l+r.."[!e- 5. Solve the following problems. (Show work) a) The ratio of two supplementary angles is 4:5' Find the 4b\ = lto QK' [ trc) =*<> 4D:J2 Y=& ffoo I 1oo" two pieces. The ratio of the two pieces is 5:7. How big are the two pieces? c) A 3 foot stick is broken into tX.+17c=7b [>6: I L Y*-3 2:3. Find the measures of each angle. measures of each angle. VY+ 9Y b) The ratio of two complementary angles is d) ls the largest angle acute, right or obtuse in a triangle that has angles measures in ratio, 2:3:4? ,( -rf z 0)=L I (9-in",717n e) Points A, B, C, and D are placed in alphabetical order on a line so that AB = ZBC = CD. What is the ratio BD : AD? A a."# ggpe BC D f) Points A, B, and C are placed in alphabetical order on line so that 3AB : AC. What is the ratio of AB : BC? a 3 € ,9 g) Two numbers are in ratio 7 : 3. The sum of the two numbers is 36. What is the largest number? av +3 x, = 5 t loY=3b 1>3, b t b"u) h) Three numbers are in the ratio of 2 : 5 : 3. lf the largest number is 65. What is the smallest number?