Ratios and Proportions
Solving Proportions Using Cross Products
Solving Percent Problems
Rewrite Equations and Formulas
Grab Bag
100
Your friend makes 20 brownies for you and your friends, but some of you are alergic to nuts so she made 5 without nuts. Write a ratio and then simplfy it to show the number of brownies with nuts to the ones without.
5/15=1/3 20-5=15 5/15 /5 /5 1/3
100
Solve this proportion using cross products: 2/3=x/9
x=6 2/3=x/9 2*9=18 3*x=18 /3 /3 18/3=6
100
x/50=50/100
x=25 x/50=50/100 100x=2500 50*50=2500 2500/100=25 x=25
100
Solve ax+b=c for x.
ax+b=c -b -b ax=c-b /a /a x=(c-b)/a
100
What is wrong with the following answer: If Billy sold a small car for $200 and a big one for $475 what percent of the big car is the small car? 475/200=x/100 200x=47500 /200 /200 x=237.5%
In the proportion you have to have part over whole on both sides and in the answer it has whole over part and part over whole on opposite sides of the equals sign.
200
You are baking cookies. A normal recipe requires 100 chocolate chips (2 cups). If you want to make a smaller recipe that is only 1 cup of chocolate chips. How many chocolate chips will you need.
x=50 100/2=x/1 (cross multiply) 2x=100 /2 /2 x=50
200
If you are drawing a picture of your house, but you have to draw it to scale. Your house is 50 ft tall. For every inch of your drawing is 5 feet. Write a proportion to find how tall your house is in the picture.
x=10 inches x/50=1/5 50*1=50 x*5=50 /5 /5 x=10
200
What percent is 55 is 11?
x=20 11/55=x/100 55x=1100 11*100=1100 1100/55=20 x=20
200
Solve ab-c=x for b.
ab-c=x +c +c ab=x+c /a /a b=(x+c)/a
200
What percent of 46 is 3?
3/46=x/100 300=46x /46 /46 x=6.52%
300
Jerimiah eats 5 jelly beans. He gets another bag of jelly beans and eats 5 more. If there are 10 jelly beans not eaten from the two bags, and each bag has an equal number of jelly beans. How many jelly beans are in one bag at the begining.
x=10 5/x=10/20 100=10x /10 /10 x=10
300
11/w=33/w+24
w=12 11/w=33/w+24 33w=11w+264 -11w -11w 22w=264 /22 /22 w=12
300
What percent of 75 is 27?
x=36 27/75=x/100 75x=2700 /75 /75 2700/75=36
300
Solve ax=bx+c for b.
ax=bx+c -c ax-c=bx /x /x (ax-c)/x=b
300
Solve the following equation for c: y(x+zr)=xc
c=y+yzr=c y(x+zr)=xc yx+yzr=xc /x /x y+yzr=c
400
In the graph below it shows the recipe to make a casserole. You want to figure out how many cans of chicken stock you will need. Using the data set up a proportion and find out how many cans you would need if you wanted to serve a large family. Size: Cans of Chicken Stock 2 people 2 cans (Small) ------------------------------------------- 7 people x (Large)
4 cans 2/2=x/7 /2 /2 x=3.5 so 4 cans
400
You are creating a map for a world Atlas book. They told you that they want you to make a map for a city in Europe for tourists. They told you the land was about 6.78*10^5 miles wide. If you want to make it on a map where 1 inch equals 100 miles how wide would your paper be.
x=miles wide x/6.78*10^5=1/100 x/678,000=1/100 x*100=678,000 678,000*1=678,000 678,000/100=6,780 inches
400
41.8 is 44% of what number?
x=95 41.8/x=44/100 44x=4180 /44 /44 4180/44=95 x=95
400
Solve for a in 2a-bx=c when x equals 5.
2a-bx=c 2a-b(5)=c +b(5) +b(5) 2a=c+b(5) /2 /2 a=(c+b(5))/2
400
The elevator at John Handcock Center in Chicago takes the passengers 150ft. in 5 seconds. If they press the button for the 96'th floor which is 1559 ft how long does it take them to get there from the bottom floor?
t=51.96 seconds 5/150=t/1559 150t=7795 /150 /150 t=51.96 seconds
500
Bill's Car and Stuff Shop sells cars and stuff. Bill's cars have sold 4^3% more than last year. Set up a proportion and find out how many he sold this year if he sold 46 last year.
4^3=64 x/46=64/100 *100 *100 100x/460=640 *460 *460 100x=294,400 /100 /100 29,440 more 46+29,440=29,486 cars
500
You and your friend are working at a school fund raiser making popcorn. The machine's instructions says that you should add 1 cup of popcorn kernals for every 4 bags you wanted to make. Your friend put in 3 cups because she wanted to make 2^4 bags and have enough to snack on later what did she do wrong and what should she have done.
She should have done 4 or more cups. They didn't even have enough to fill all of the bags let alone have some to snack on as well.
500
In a school transportation survey of 225 students 18 of the students surveyed said they walked to school. 40 students said they carpooled. 50 students take the bus. The rest of the students drive. What percent of the students walk to school.
x=8 18/225=x/100 225x=1800 /225 /225 1800/225=8 x=8
500
The surface area of S=pi(r)l. Solve for l when S= 283 cm squared and r=5cm.
l=18.0254777 283=pi(5)l 283=15.7(l) /15.7 /15.7 l=18.0254777
500
A car traveling 50 miles a hour goes 15 miles farther in the same amount of time as a car traveling 30 miles per hour. Find the diestace each car travels.
50mph=37.5miles 30mph=22.5miles 50-30=20mph 20mph=15 miles 30=15mph+1/2 of 20mph 15/2=7.5 50=30mph+20mph 30mph=22.5 miles 22.5+15=37.5
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