Word Problems I
Three consecutive numbers have a sum of 75. What is the smallest number?
The smallest number is 24.
What is the next number in the sequence?
2, 5, 10, 17, ___
26
(+3, +5, +7, +9)
Which is larger?
101/102 and 100/101
101/102 > 100/101
A number is increased by 20% and then decreased by 20%.
Is the final number equal to the original? Explain
No, it is less. (Example: 100 → 120 → 96)
I am a two-digit number.The sum of my digits is 10.The difference of my digits is 4.64
(6 + 4 = 10, 6 − 4 = 4)What is the number?
64
(6 + 4 = 10, 6 − 4 = 4)
A number is multiplied by 3/4 and then 2/5 of the result is subtracted. The final answer is 9/20. What the original number?
1
If the side lengths of a triangle are three consecutive odd numbers, and the perimeter is 51 cm, what is the length of the longest side?
The longest side is 19 cm.
If three consecutive even numbers have a sum of 84, what is the largest number?
The largest number is 30.
There are 8 cubes in a box. Each cube has one of the following numbers written on it:
2, 5, 8, 10, 14, 17, 18, 20
Maksim randomly takes one cube from the box without looking.What is the probability that the number written on it is odd?
1/4
7x + 42 = -3x - 28
x = -7
Which is greater: 40% of 80 or 32% of 100?
They are equal
Neal wants to buy a puppy. He pays $150 up front and then pays $5 every week after for the next year (a year has 52 weeks). How much will he end up paying at the end of the year?
He will pay $410.
The length of the Princeton basketball court is five more than twice the width. If the perimeter of the court is 112 meters, how long is the court?
39 length
The product of 33 positive integers is 33
What the sum of the numbers?
33 has only teo factors which one 1; 3 and 11. Both of them prime
All the remaining numbers must be 1, because multiplying by 1 does not change the product.
Sum:
31×1 + 3 + 11 = 31 + 14 = 45
(x - 5)(x + 3) = 0
x = 5 or x = -3
((x-¹y²)) -¹
(———)
(x²y-³)
x3
———
y⁵
If the average of four consecutive even numbers is 49, what are all four numbers?
46, 48, 50, 52
Three positive numbers , , and have sum equal to 3.
Each of them is divided by the sum of the other two numbers.
The three results are then added together.
Prove that the final sum is at least 1.5, and determine exactly when this minimum value is achieved.
The final sum is at least 1.5, which is proven by Nesbitt's Inequality. The minimum value of 1.5 is achieved if and only if a=b=c, which, with the given sum, means a=b=c=1
x^2 - 9x + 18 = 0
x = 6 or x =3
Simplify the following expression:
(0.002)³
8× 10-⁹
(2×10-³)³= 8×10-⁹