Proportions
Ratios
Exponents
Systems of Equations
SAT Real Questions
100
True or False. Ratios are what make up proportions.
True. A proportion is simply a statement that two ratios are equal. We can use cross multiplication to test whether two ratios are equal and form a proportion.
100
What are the 3 ways to correctly write a ratio?
1. 1:2
2. 1/2
3. 1 to 2
100
35=?
243.
3*3*3*3*3=243
100
The solution to the system of equations:
r + s = -6
r - s = -10
R= -8
S= 2
100
3x + 4y = −23
2y − x= −19
What is the solution (x, y) to the system of equations above?
A) (−5, −2)
B) (3, −8)
C) (4, −6)
D) (9, −6)
B) (3, -8)
200
Ernie makes candles that are 14 cm tall. Each candle burns 8 hours before going out. He is wondering how many hours a 21 cm tall candle can burn for.He assumes that the relationship between the height of a candle and number of hours it burns (h) is proportional. How long can a 21 cm tall candle can burn for?
12 hours.
14 cm/21 cm=8 hour/ x hours
14x= 21*8
14x=168
x=12
200
A backyard pond has 12 sunfish and 30 rainbow shiners. Write the ratio of sunfish to rainbow shiners in simplest form .
Write the ratio as a fraction.
12/30
Now reduce the fraction .
2/5
So the ratio of sunfish to rainbow shiners is 2:5 .
200
Solve For: (2x3)2
4x6
200
Solve using elimination.
8x-2y=26
3x=2y=29
x=5
y=7
200
The recommended daily calcium intake for a 20-year-old is 1,000 milligrams (mg). One cup of milk contains 299 mg of calcium and one cup of juice contains 261 mg of calcium. Which of the following inequalities represents the possible number of cups of milk m and cups of juice j a 20-year-old could drink in a day to meet or exceed the recommended daily calcium intake from these drinks alone?
A.
B.
C.
D.
A.
Multiplying the number of cups of milk by the amount of calcium each cup contains and multiplying the number of cups of juice by the amount of calcium each cup contains gives the total amount of calcium from each source. You must then find the sum of these two numbers to find the total amount of calcium. Because the question asks for the calcium from these two sources to meet or exceed the recommended daily intake, the sum of these two products must be greater than or equal to 1,000.
300
Pamela drove her car 99 kilometers and used 9 liters of fuel. She wants to know how many kilometers (km) she can drive with 12 liters of fuel. She assumes the relationship between kilometers and fuel is proportional.
How many kilometers can Pamela drive with 12 liters of fuel?
132km. If we set up the proportion as 99km/9l=x/12, we will be able to cross multiply and have (99)(12)=9x. Then, multiply 99 by 12 and get 1,188=9x. Divide by 9 on both sides to get x by itself and x=132km.
300
Jack the Giant is very hungry and upset! The villagers decide to make him a cake to get rid of his hunger. The recipe for calls for butter and sugar in the ratio 22:33. If you're using 66 cups of butter, how many cups of sugar should you use?
The ratio 22:33 means that for every 22 cups of butter, you should use 33 cups of sugar.
Here you're using 66 cups of butter, so you need to multiply by the amount of sugar by 33 .
66×33= 2, 178
After that divide by 22 and x=99. So, you need to use 99 cups of sugar.
300
(2y103) x (2y106) x (2y1012) = ?
8y1021
Explanation:
The three two's multiply to become 8 and the powers of 3, 6 and 12 add up to 21.
300
Solve using elimination or substitution.
−9y+4x−20=0
−7y+16x−80=0
x=5
y=0
300
The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children and how many adults attended?
Number of adults: a
Number of children: c
total number: a + c = 2200
total income: 4a + 1.5c = 5050
Now solve the system for the number of adults and the number of children. I will solve the first equation for one of the variables, and then substitute the result into the other equation:
a = 2200 – c
4(2200 – c) + 1.5c = 5050
8800 – 4c + 1.5c = 5050
8800 – 2.5c = 5050
–2.5c = –3750
c = 1500
Now I can back-solve for the value of the other variable:
a = 2200 – (1500) = 700
To answer the original question, there were:
1500 children and 700 adults.
400
Oscar loves cheese burgers. He enters a 24 hour cheese burger eating contest. During the contest Oscar eats a cheese burger every 15 minutes. How many cheese burgers will he eat during the entire contest?
96 cheeseburgers.
24 hours = 1440 minutes
So, 1 cheeseburger/15=x cheeseburgers/1440 minutes. Cross multiply and you will get 15x=1440. Divide by 15 on both sides and x=96 cheeseburgers.
400
You randomly draw a tiles from a bag that contains 8 I tiles, 4 Q tiles, 12 Y tiles, 3 E tiles, and 3 A tiles 16 W tiles, 1 Z tile and 7 T tiles. Write the ratio, in simplest form, of vowels to non-vowels in 3 different ways.
The number of vowels drew were 26 and the number of non-vowels are 27. You could write the ratio as:
26:27;
26 to 27;
26/27
400
Simplify: 42g1636p1296w1/7g109p1112w3
6g64p/8w2.
First you would divide the coefficients (numbers). So you would divide 42/7, 36/9, and 96/12.
You will get 6g164p128w1/7g109p11w3
Then subtract the exponents that have the same base, in this case you would subtract 16-10, 12-11, and 3-1.
You're final answer will be 6g64p1/8w2.
400
(1/3)x + (1/4)y = 10
(1/3)x - (1/2)y = 4
x= 24
y=8
400
Wyatt can husk at least 12 dozen ears of corn per hour and at most 18 dozen ears of corn per hour. Based on this information, what is a possible amount of time, in hours, that it could take Wyatt to husk 72 dozen ears of corn? (Hint: It's 2 values)
The correct answer is any number between 4 and 6, inclusive. Since Wyatt can husk at least 12 dozen ears of corn per hour, it will take him no more than 72/12=6 hours to husk 72 dozen ears of corn. On the other hand, since Wyatt can husk at most 18 dozen ears of corn per hour, it will take him at least 72/18=4 hours to husk 72 dozen ears of corn. Therefore, the possible times it could take Wyatt to husk 72 dozen ears of corn are 4 hours to 6 hours, inclusive. Any number between 4 and 6, inclusive, can be gridded as the correct answer.
500
Preston drove to his new college and then back home. Round trip he traveled 215 miles. Preston drives a Honda Civic and gets 35 miles for every gallon of gas. If Preston needs to make 12 round trips a year how much will it cost him in gas? Assuming the price of gas stays at $3.60 a gallon. Round to the nearest hundredth.
$265.25. Set up the proportion as 35 mi/1 gal=215 mi/x gal. Cross multiply and you will get 35x=215. Divide by 35 on both sides and x=6.14 gallons.
You're not done yet! We now know that it takes 6.1 gallons to make 1 trip to the college and back. We want to find the price for 12 round trips a year. So first, we would find how many gallons it takes for 12 trips by multiplying 6.14*12= 73.68 gallons. Lastly, convert the gallons to dollars by multiplying 73.68*3.60= $265.25.
500
Mr. Smith divides a sum of money between his three children Alex, Billy and Charlie in the ratio 3 : 2 : 7. If Charlie received $120 more than Alex, how much money did Billy receive?
Let x be the amount each receives.
7x-140=3x
7x-3x=140
4x=140
x=140/4
x=35
Billy receives two times of 2.
Therefore, he receives 35*2=$70.
500
Simplify: 
Step 1: Add the exponents. So by adding the (-3) to 3, x4 and y-2 you will get:
Step 3: Flip the negative exponents. Move every negative exponent in the numerator to the denominator and vice versa.
Step 4: Divide exponents. Divide two exponents with the same base, you keep the base and subtract the powers.
Step 5: Subtract common base exponents. In this case, the x’s ended up in the denominator because there were 2 more x’s in the denominator.
Step 6: Raise each coefficient (or number) to the appropriate power and then simplify or reduce any remaining fractions. In this case, the fraction does not reduce.
500
Solve using either elimination or substitution.
2x + 9y=0
3x + 5y=17
x= 9
y= -2
500
Each sheep has 4 legs and each chicken has 2 legs. If a farm boy counts 50 heads and 140 feet, how many sheep are there?
20 sheep.
Set x as the number of sheep and y as the number of chicken. This gives us x+y=50 and 4x+2y=140. We want to solve for x. Solving the first equation we get y=50-x. Substitute that into the second you have 4x+2(50-x)=140. Multiplying it out gives 4x+100-2x=140. So 2x+100=140. 2x=40, x=20. Giving 20 sheep.