Mathematical Reasoning Flashcards

A town's population grows by 15% and 20% during the course of two years. After two years, what percentage of the population has grown?

Answer: 38%

The population has grown by 15% and 20%, respectively. The population grows by 15%, bringing it to 115 percent of its initial size. Multiply the figure by 120 percent for the second increase. 138 percent (1.15)(1.20)=1.38 percent After two years, the population has expanded by 38%.

Mr. Frank puts aside $2,500 of his $55,000 monthly family income. What percentage of his income does he set aside for savings?

Answer: 1/22

2,500 out of 55,000 equals to 2500/5500 = 25/550 = 1/22

The average of five numbers in a row is 38. What is the smallest number?

Answer: 36

Let 𝑥 be the smallest number. Then, these are the numbers: 𝑥,𝑥+1,𝑥+2,𝑥+3,𝑥+4 𝑎𝑣𝑒𝑟𝑎𝑔𝑒=𝑠𝑢𝑚𝑜𝑓𝑡𝑒𝑟𝑚𝑠𝑛𝑢𝑚𝑏𝑒𝑟𝑜𝑓𝑡𝑒𝑟𝑚𝑠⇒38=𝑥+(𝑥+1)+(𝑥+2)+(𝑥+3)+(𝑥+4)5⇒38=5𝑥+105⇒190=5𝑥+10⇒180=5𝑥⇒𝑥=36

The number 83 is 5 less than twice a positive integer. What is the value of the integer?

Answer: 44

Let 𝑥 be the integer. Then: 2𝑥–5=83 Add 5 both sides: 2𝑥=88 Divide both sides by2:𝑥=44

One-fifth of a supplement equals an angle. What is the angle's measurement?

Answer: 30

The total of the supplement angles is 180 degrees. Let's call that angle x. As a result of x+5x=180 6x=180, divide both sides by 6:x=30.

What is the difference between a four-digit number that is the smallest and a four-digit number that is the biggest?

Answer: 8999

1000 is the smallest four-digit number, and 9999 is the largest four-digit number. 8999 is the difference.

How many inches does 11 yards, 6 feet, and 4 inches equal?

Answer: 472

11 x 36 + 6 x 12 + 4 = 472

In a class of 18 girls, the average weight is 60 kg, while the average weight of 32 boys in the same class is 62 kg. What is the average weight of that class's 50 students?

Answer: 61.28

𝑎𝑣𝑒𝑟𝑎𝑔𝑒=𝑠𝑢𝑚𝑜𝑓𝑡𝑒𝑟𝑚𝑠/𝑛𝑢𝑚𝑏𝑒𝑟𝑜𝑓𝑡𝑒𝑟𝑚𝑠 1860=1080 kg is the total weight of all the girls. The total weight of all of the boys is 3262=1984 kg. The total weight of all pupils is 1080+1984=3064 kg, with an average of 306450=61.28 kg.

Find x and compute the solution to the formula 3x=24.

Answer: 8

Divide both sides by 3 to get x by itself 3x/3 = 24/3 Simplifying: x=8 To check the answer, substitute 8 for x, 3(8)=24

Attorney A charges a flat rate of $250 for the initial consultation and $150 per hour for all additional hours spent. Attorney B costs $175 per hour and $150 for the initial consultation. Find the cost for each attorney's 26 hours of work. Which offer is better?

Answer: Attorney A

Total charge for 26 hours with Attorney A: 250+25×150=250+3750= 4000 Total charge for 26 hours with Attorney B: 150+26×175=150+4550=4700 For 26 hours of work, Attorney A charges $4000, while Attorney B charges $4700. In this case, Attorney A's total charge is lower, making Attorney A the better deal for 26 hours of work.

Kwame discovered that enchiladas were the food that 20 out of 50 pupils in the lunch line liked the most. 520 pupils make up Kwame's middle school. Estimate how many people prefer enchiladas.

Answer: 208

Proportion of pupils who prefer enchiladas in the lunch line: 20 pupils/50 pupils = x pupils/ 520 pupils Now, cross-multiply: 50x = 20×520 Solve for x: x = 20×520 / 50 x= 208

Simplify the given expression: 3+(3−8)^2 −7

Answer: 21

First, solve the expression inside the parentheses: 3+(3−8)^2 −7 =3+(−5) ^2 −7 Next, calculate the square of -5: =3+25−7 Now, perform the addition and subtraction: =28−7 Finally, perform the subtraction to get the simplified result: =21

Which inequality corresponds to a number that is not higher than 34.

Answer: x≤34

The symbol "≤" represents "less than or equal to," so the inequality x≤34 includes all values of x that are less than or equal to 34. Therefore, any number equal to or less than 34 satisfies this inequality.

Compute: -3x < 12

Answer: x>-4

Divide -3 to each side. -3x/-3 Each side was divided by -3, hence the inequality symbol's direction must be changed. The answer is x > -4.

Each of Ela's baked pies costs $5. Ela must make a sale ____ in an effort to make $200.

Answer: 40 pies

The formula we employ to determine the answer is shown below: 200÷5=40

There is a more than two-thirds chance of rain on Saturday, according to the local weather report. What probability is it that Saturday will be rainy?

Answer: 66 %

The probability of an event occurring ranges from 0 to 1, where 0 means the event is impossible, and 1 means the event is certain to happen. Since the probability is greater than 2/3, we know that it is more likely to happen than not. Therefore, the likelihood that it will rain on Saturday is greater than 2/3 or more than 66.67%.

Simplify the given expression: 9(9−10r)+(−8−2r)

Answer: 73−92r

Distribute the 9 to both terms inside the first parentheses: 81−90r+(−8−2r) Combine like terms: 81−90r−8−2r Now, combine the constants and the terms with: 73−92r

Find the difference. −83−17+87=

Answer: -13

To find the difference, we need to subtract the sum of the numbers: −83−17+87=−100+87=−13 So, the difference is −13.

Find the difference. 8695+(−3)−(6290−4233)

Answer: 6635

Simplify the expression inside the second set of parentheses: 8695+(−3)−(6290−4233)=8695+(−3)−2057 Perform the subtraction inside the parentheses: 8695+(−3)−2057=8695+(−3)−2057=8695+(−2060) Finally, perform the addition and subtraction: 8695+(−2060)=6635