Need Help on finding the consecutive integers

Question

Find three consecutive integers such that the sum of 3 times the smallest and 5 times the largest is 90.

Answer 1

x, x + 1, x + 2 are consequtive integers. Then 3x + 5(x + 2) = 90; 8x = 80, x = 10.

So answer: 10, 11, 12

Answer 2

We know that integers are whole numbers (no fractions or decimals). An example of three consecutive integers is 1, 2, and 3, since each integer is one more than the integer before it, except for the starting value.

Let n = first integer.

Therefore,

second integer = n + 1

third integer = (n + 1) + 1 = n + 2

With our smallest integer being the first integer and our largest integer being the third integer, we now simply plug these into the word problem and solve for n.

3*n + 5*(n + 2) = 90

3n + 5n + 10 = 90

8n + 10 = 90

8n = 80

n = 10

Now we take our value n = 10 to solve for our integers.

First integer = n = 10

Second integer = n + 1 = 10 + 1 = 11

Third integer = n + 2 = 10 + 2 = 12

Our final answer for our three consecutive integers is: 10, 11, 12.