The sum of a number and twice its reciprocal is 3. What is the number?

unknown values: x

equation: x + 2/x = 3

answer: 2 or 1

Given a six digit number whose last digit is 1. If you place 1 as the first digit the resulting number is 1/3 that of the original one. Determine the original number.

unknown values: 100000*k+10000*x+1000*y+100*z+10*l+1

equation: (100000+10000*x+1000*y+100*z+10*l+1)/3=100000*k+10000*x+1000*y+100*z+10*l+1

answer: 428571

What three consecutive numbers have a sum which is 1/5 of their product

unknown values: x,x+1,x+2

equation: x+x+1+x+2=x*(x+1)*(x+2)/5

answer: 3; 4; 5 or -1; 0; 1 or -5; -4; -3

A sum of $1400 is to be divided between two people in the ratio 3:5. How much does each person receive?

unknown values: 3*x,5*x

equation: 3*x+5*x=1400

answer: 525; 875

Find the nth number in the sequence 1, 5, 13, 25, 41

unknown values: x

equation: x = 1 + 2(n-1)n

answer: 1 + 2(n - 1)n | 2n ^ 2 - 2n + 1 | n ^ 2 + (n - 1) ^ 2

The sum of the digits of a two-digit numeral is 8. If the digits are reversed, the new number is 18 greater than the original number. Find the original number.

unknown values: 10*x+y

equation: x+y=8

equation: 10*y+x=18+10*x+y

answer: 35

There were 5 times as many boys as girls at the party. Also, the number of boys was 100 less than 15 times the number of girls. How many boys and girls came to the party?

unknown values: x,y

equation: x=5*y

equation: x+100=15*y

answer: 50; 10

A two digit counting number has a value of 8 times the sum of its digits. If 6 times the units digit is 5 more than the tens digit, what is the number?

unknown values: 10*x+y

equation: 10*x+y=8*(x+y)

equation: 6*y-5=x

answer: 72

The sum of the digits of a two-digit number is 7. The original two-digit number is 3 less than 4 times the number with its digits reversed. Find the original two-digit number.

unknown values: 10*x+y

equation: x+y=7

equation: 10*x+y=4(10*y+x)-3

answer: 61

Find three consecutive positive integers such that the product of the first and third, minus the second, is 1 more than 4 times the third.

unknown values: x,x+1,x+2

equation: x*(x+2)-(x+1)=1+4*(x+2)

equation: x>0

answer: 5;6;7