一个美术生
the tens digit of a two-digit number exceeds twice the units digit by 1. if the digits are reversed, the sum of the new number and the original number is 143. find the original number.
unknown values: x
equation: a = 2*b + 1
equation: 10*a+b=x
equation: (10*b+a)+x=143
answer: 94
A two digit number is 7 times its unit digit. If 18 is added to the number, its digits are reversed. Find the number.
unknown values: n
equation: n = 10*a + b
equation: n = 7*b
equation: n + 18 = 10*b + a
answer: 35
The square of a number decreased by 5 is the same as 3 more than 7 times the number. Find the number.
unknown values: x
equation: x^2 - 5 = 3 + 7*x
answer: 8 or -1
Five times the first of three consecutive even integers is four less than three times the third integer. Find the smallest even integer
unknown values: 2*k-2
equation: 5(2*k-2) = 3(2*k+2)-4
answer: 4
the sum of the digits of a 2-digit number is 7. The tens digit is one less than 3 times the units digit. Find the number.
unknown values: x
equation: x = 10*a+b
equation: a+b=7
equation: a = 3*b - 1
answer: 52
The tens digit of a 2-digit number is 9 less than twice the units digit. If the sum of the 2 digits is 18, what is the number ?
unknown values: n
equation: n = 10*t + u
equation: t = 2*u - 9
equation: t + u = 18
answer: 99
Find three consecutive integers such that 3 times the first integer plus the second integer minus 2 times the third integer is 9.
unknown values: k,k+1,k+2
equation: 3*k + (k+1) - 2(k+2)=9
answer: 6; 7; 8
four times the smallest of three consecutive odd integers is five more than three times the largest. What is the sum of these consecutive odd integers?
unknown values: x
equation: x = (2*k+1) + (2*k+3) + (2*k+5)
equation: 4(2*k+1) = 5 + 3(2*k+5)
answer: 57
Three times the opposite of a number is 40 greater than 5 times number. What is the number?
unknown values: n
equation: 3((-1)*n) = 40 + 5*n
answer: -5
Find a number that is 32 more than its opposite
unknown values: n
equation: n = -1 * n + 32
answer: 16