Answer:
As the first number is 5, the second will be 7, and the third will be 9.
Step-by-step explanation:
First, let's break down what the information is telling us.
"three consecutive odd integers" means each number is 2 away from each other. So if we were to assign the variable x as the first number, the second would be x + 2 and the third would be x + 4
"sum of the smallest number and twice the middle number" refers to adding the first number and 2 times the second number. So we would write:
x + 2(x + 2)
"is 10 more than the largest number" connects the second part to an equation. This is saying the third number plus 10. So for this, we would write:
(x + 4) + 10
Now we join the information that we have written mathematically into an equation. Since we have an equation, we can solve for the first number, and hence the second and third numbers.
x + 2(x + 2) = (x + 4) + 10
x + 2x + 4 = x + 14
3x + 4 = x + 14
2x = 10
x = 5
As the first number is 5, the second will be 7, and the third will be 9.
The key idea for solving this question is to define a variable and connect it to an equation using the information provided. Try to think about how much information is needed and how many variables need to be defined.
