Question

The heights in inches of three basketball players are 3 consecutive integers. If the sum of twice the 1st, 3 times the 2nd, and the 3rd is 437, what are the three heights.

Answer 1

Conditions

The heights in inches of three basketball players are 3 consecutive integers. If the sum of twice the 1st, 3 times the 2nd, and the 3rd is 437, what are the three heights.

Solution

As we can notice, the heights in inches of three basketball players are 3 consecutive integers. So if we consider, that height of $1^{\text{st}}$ is $x$, then the height of $2^{\text{nd}}$ is equal to $(x+1)$, the height of $3^{\text{rd}}$ is $(x+2)$. And now we must sum these 3 values, $1^{\text{st}}$ will be powered by 2, $2^{\text{nd}}$ by 3, and $3^{\text{rd}}$ by 1, and total is 437:

$$2x + 3(x + 1) + x + 2 = 437$$ $$6x = 432$$ $$x = 72$$

Then, the height of $1^{\text{st}}$ is 72, $2^{\text{nd}} - 73$, $3^{\text{rd}} - 74$ inches.

**Answer: 72, 73, 74**