when twice a number is decreased by 8, the result is the number increased by 7. find the number?

unknown values: x

equation: 2*x - 8 = x + 7

answer: 15

3 less than 5 times a number is 11 more than the number? Find the number.

unknown values: n

equation: 5*n - 3 = 11 + n

answer: 7/2 | 3.5

If x-y = 5 and x^2 + y ^ 2 = 15 what is the value of xy?

unknown values: x*y

equation: x-y = 5

equation: x^2 + y^2 = 15

answer: -5

if 5 times the smaller of two numbers is subtracted from twice the larger, the result is 16. if the larger is increased by 3 times the smaller, the result is 63. find the larger number.

unknown values: y

equation: 2*y - 5*x = 16

equation: y + 3*x = 63

answer: 33

Using the equations below, find the value of F if A= 5A+B=CC+D=EE+A=FB+D+F=30

unknown values: f

equation: a = 5

equation: a + b = c

equation: c + d = m

equation: m + a = f

equation: b + d + f = 30

answer: 20

the first three terms of an arithmetic sequence are (12-p), 2p, (4p-5) respectively where p is a constant.Find the value of p

unknown values: p

equation: 2*p - (12-p) = (4*p-5) - 2*p

answer: 7

there are four consecutive odd integers. the sum of the first and the second numbers is 96. what are the integers?

unknown values: n,n+2,n+4,n+6

equation: n + (n+2) = 96

answer: 47; 49; 51; 53

write three prime numbers that add up to 100

unknown values: p,q,r

equation: p + q + r = 100

equation: is_prime_number(p, q, r)

answer: {2; 19; 79} or {2; 31; 67} or {2; 37; 61}

If the product of -3 and the opposite of a number is decreased by 7, the result is 1 greater than the number. What is the number?

unknown values: n

equation: -3*(-1 * n) - 7 = 1 + n

answer: 4

In an arithmetic series, the terms of the series are equally spread out. For example, in 1 + 5 + 9 + 13 + 17, consecutive terms are 4 apart. If the first term in an arithmetic series is 3, the last term is 136, and the sum is 1,390, what are the first 3 terms?

unknown values: a,a+d,a+2*d

equation: a = 3

equation: a + (n-1)d = 136

equation: (a + 136)n/2 = 1390

answer: 3; 10; 17