word problem

[nativewind]

the product of two consecutive integers is 8 less than 8 times their sum. what are the integers?

 

[soroban]

Hello, nativewind!

The product of two consecutive integers is 8 less than 8 times their sum.
What are the integers?

We have two consecutive integers.

Let \(\displaystyle x\) = first integer, \(\displaystyle x+1\) = next integer.

. . \(\displaystyle \underbrace{\text{ Product of the two integers }}_{x(x+1)} \underbrace{\text{ is }}_{=} \underbrace{\text{ 8 times }}_{8 \times} \underbrace{\text{ their sum }}_{x+(x+1)} \underbrace{\text{ minus 8 }}_{-\;8}\)

\(\displaystyle \text{The equation is: }\;x(x+1) \;=\;8(2x+1) - 8\)

Now solve the quadratic . . .