Cymath AI Math Solver

Challenge 1: Arithmetic Puzzle

Instructions
Solve the arithmetic puzzle below by using addition, subtraction, multiplication, and division to find the missing number.

Puzzle
• Find the missing number in the sequence: 8, 4, 2, 1, _?

Hint
Consider the operations applied between each number in the sequence.

Challenge 2: Number Sequence

Problem
Identify the pattern in the following number sequence and predict the next number:
2,4,8,16,.....

Hint
Consider the mathematical operations involved in progressing from one number to the next in the sequence.

Challenge 3: Logic Puzzle

Puzzle Description
In a small village, there are three houses in a row, each painted a different color: red, blue, and green. Each house is owned by a different person: Alex, Blake, and Casey. Each person owns a different pet: a cat, a dog, and a bird.

Clues
1. Alex lives in the red house.
2. Blake owns the dog.
3. The greenhouse is to the left of the blue house.
4. The person with the bird lives next to the person with the cat.

Task
Determine the color of each house, who owns each house, and which pet each person owns.

Challenge 4: Probability Question

Scenario
In a standard deck of 52 playing cards, calculate the probability of drawing an Ace as the first card.

Solution
• There are 4 Aces in a deck of 52 cards.
• Probability of drawing an Ace = ( \frac{4}{52} = \frac{1}{13} )
• Therefore, the probability is approximately 0.0769 or 7.69%.

Challenge 5: Word Problem

Problem Statement
A farmer has a total of 50 animals consisting of chickens and cows. If the total number of legs is 140, how many chickens and cows does the farmer have?

Solution Approach
• Let ( x ) be the number of chickens and ( y ) be the number of cows.
• Each chicken has 2 legs and each cow has 4 legs.
• Translate the word problem into the following equations:
⚬ Total animals: ( x + y = 50 )
⚬ Total legs: ( 2x + 4y = 140 )
• Solve the system of equations to find the values of ( x ) and ( y ).

Challenge 6: Algebraic Equation

Problem Statement
Solve the following algebraic equation to find the value of ( x ):
[
3x + 5 = 20
]

Solution Steps
1. Subtract 5 from both sides:[ 3x + 5 - 5 = 20 - 5
]Simplified, this becomes:[ 3x = 15]
2. Divide both sides by 3:[\frac{3x}{3} = \frac{15}{3}] 

Simplified, this becomes:[ x = 5]

Conclusion
The value of ( x ) is 5.

Challenge 7: Geometry Problem

Task
Calculate the area of the given shape using the appropriate geometric formulas.

Steps
1. Identify the type of geometric shape.
2. Use the relevant formula to calculate the area.
3. Ensure all measurements are in the same units before calculating.
4. Solve the problem within 30 seconds.

Challenge 8: Fractions and Decimals

Task
• Convert fractions to decimals.
• Convert decimals to fractions.
• Solve related problems involving these conversions.

Example Problems
• Convert ( \frac{3}{4} ) to a decimal.
• Convert 0.75 to a fraction.
• If ( \frac{2}{5} ) of a number is 10, what is the number?

Tips
• Remember: Divide the numerator by the denominator to convert a fraction to a decimal.
• To convert a decimal to a fraction, write the decimal as a fraction with a denominator of 10, 100, etc., and simplify.

Challenge 9: Time and Distance

Problem
A car travels at a constant speed of 60 km/h. How far does it travel in 30 minutes?

Solution
To solve this problem, use the formula: Distance = Speed × Time
• Speed: 60 km/h
• Time: 30 minutes = 0.5 hours
Distance = 60 km/h × 0.5 hours = 30 km
Therefore, the car travels 30 kilometers in 30 minutes.

Challenge 10: Data Interpretation

Task
Interpret the data from the chart below to determine the trend in sales over the years. Answer the following question: In which year did the sales peak?

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