The sum of two numbers is twice their difference. The larger number is 6 more than twice the smaller. Find the numbers.

unknown values: x,y

equation: x+y=2*(x-y)

equation: x=6+2*y

answer: {18; 6} | {18; 6} or {-18/5; -6/5} | {18; 6} or {-3.6; -1.2}

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

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

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

find five consecutive odd integers such that the sum of the first and fifth number is one less than three times the fourth number

unknown values: 2*k-1,2*k+1,2*k+3,2*k+5,2*k+7

equation: (2*k-1+2*k+7)=3*(2*k+5)-1

answer: -9;-7;-5;-3;-1

the second of three numbers is 8 more than the first, and the third number is 3 less than 3 times the first. if the third number is 15 more than the second, find the three numbers.

unknown values: x,y,z

equation: y = 8 + x

equation: z = 3*x - 3

equation: z = 15 + y

answer: 13; 21; 36

When fifteen is subtracted from four times the sum of seven and twice some number, the result is 45

unknown values: x

equation: 4*(7+2*x)-15=45

answer: 4

Find four consecutive integers such that twice the first subtracted from the sum of the other three integers is sixteen.

unknown values: x,x+1,x+2,x+3

equation: (x+1+x+2+x+3)-2*x=16

answer: 10;11;12;13

Find four consecutive integers such that twice the first subtracted from the sum of the other three is 16.

unknown values: k,k+1,k+2,k+3

equation: (k+1)+(k+2)+(k+3)-2*k=16

answer: 10; 11; 12; 13