Question

The product of two consecutive positive integers is 90. Find the integers.

Answer 1

I think in this case I would use common sense. 9 and 10 work instantly :)

Answer 2

Let's use algebra and variables to solve this problem.

Let x be the first integer and x+1 be the second integer.

According to the problem, their product is 90, so:

x(x+1) = 90

Expanding the left side:

x^2 + x = 90

Now we have a quadratic equation that we can solve by factoring or using the quadratic formula. However, we can also guess and check since the factors of 90 are not too many.

Some possible pairs of factors that multiply to 90 are:

1 x 90 = 90
2 x 45 = 90
3 x 30 = 90
5 x 18 = 90
6 x 15 = 90
9 x 10 = 90

We want consecutive integers, so only the pair 9 x 10 works.

Therefore, x = 9 and x+1 = 10.

The two consecutive positive integers that have a product of 90 are 9 and 10.

Answer 3

Yes, that's correct! Sometimes using common sense or intuition can make the problem easier and faster to solve. In this case, recognizing that 9 and 10 are consecutive integers whose product is close to 90 could lead to the answer without having to use algebra or guess and check.