Question

Three consecutive odd numbers are such that if you subtract the product of the smaller two from the product of the greater two, the result will be 76. Find these numbers.

Answer 1

Answer:

17,   19   and   21

Step-by-step explanation:

be grateful that I gave you the answer

Answer 2

Answer:

37, 38, and 39

Step-by-step explanation:

Write the equation by converting words into math symbols:

• consecutive means n, n+1, and n+2
• subtract -
• product *
• result is =

This means "the product of the smaller two" is n(n+1).

This also means "the product of the greater two" is (n+1)(n+2)

They are subtracted from each other and equal to 76. So it becomes

(n+1)(n+2) - n(n+1) = 76

Write and solve:

$(n+1)(n+2) - n(n+1) = 76\\n^2+n+2n+2-n^2-n=76\\n+2n+2-n=76\\2n+2=76\\2n=74\\n=37$

The smallest number is 37. The next is 38. The last is 39.