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Problem Templates

A number increased by x is y. n + x = y

A number decreased by x is y. n - x = y

x more than a number is y. x + n = y

x less than a number is y. x - n = y

A fraction of a number is y. f·n = y

The sum of a number and x is y. n + x = y

The product of x and a number is y. x·n = y

The quotient of a number and x is y. n/x = y

x times a number is y. x·n = y

x is equal to the product of y and some number. x = y·n

The difference of a number and x is equal to y. n - x = y

x is equal to the quotient of a number and y. x = n/y

A fraction of a number increased by x is y. f·n + x = y

A fraction of a number decreased by x is y. f·n - x = y

x times a number increased by y is z. x·n + y = z

x times a number decreased by y is z. x·n - y = z

The quotient of a number and x increased by y is z. n/x + y = z

One number is x times another. Their sum is y. n + (x·n) = y

x more than y times a number is z. y·n + x = z

x less than y times a number is z. y·n - x = z

One of two numbers is x more than the other. The sum of the numbers is y. n + (n + x) = y

The sum of two numbers is y. One number is x less than the other. n + (n - x) = y

The product of two numbers is y. One number is x less than the other. n·(n - x) = y

x times the sum of a number and y times the number is z. x(n + y·n) = z

The sum of two numbers is y. The larger number is x times the smaller number. n + (n·x) = y

x times a number equals y less than z times the number. x·n = (z·n) - y

x times the difference of y minus a number is z. x·(y - n) = z

One of two numbers is a fraction of the other number. The sum of the numbers is y. n + (f·n) = y

The sum of two numbers is x. The difference of the same two numbers is y. n - (x - n) = y

The difference of two numbers is z. The larger number is y more than x times the smaller number. (x·n + y) - n = z

The greater of two numbers is x less than y times the smaller. Their sum is z. (n·y - x) + n = z

The product of x and some number is equal to the sum of that number and y. x·n = n + y

One number is x more than another number. The sum of the larger number and twice the smaller number is y. (n + x) + 2n = y

When a number is divided by x, the result is y. n/x = y

If the product of x and a number is increased by y, the result is z. x·n + y = z

x more than y times a number is equal to the number increased by z. y·n + x = n + z

One number x more than another number. The sum of y times the larger number and z times the smaller number is w. (y·(n + x)) + (z·n) = w

The sum of three numbers is x. The largest number is y times the smallest, and the smallest is z less than the middle number. n + (n + z) + (n·y) = x

The sum of three consecutive numbers is y. n + (n + 1) + (n + 2) = y

The sum of three consecutive odd numbers is y. n + (n + 2) + (n + 4) = y

The sum of three consecutive even numbers is y. n + (n + 2) + (n + 4) = y

The sum of the first and third of three consecutive numbers is x. n + (n + 2) = x

The sum of the largest and y times the smallest of three consecutive integers is x. (n + 2) + (n·y) = x

Find two consecutive even integers such that y times the smaller decreased by the larger is x. (n·y) - (n + 2) = x

Find two consecutive odd integers such that y times the larger decreased by the smaller is x. ((n + 2)·y) - n = x

x more than the second of three consecutive even integers is the same as the difference between the third and y times the first. (n + 2) + x = (y·n) - (n + 4)

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