Two siblings are comparing their ages, which are consecutive, odd integers.

Question

Two siblings are comparing their ages, which are consecutive, odd integers. They find that the product of their ages is just one less than eight times the sum of their ages. Let n be the age of the younger sibling.

Write an equation using n that models the information given in the problem.

Answer 1

Ok, so basically this is a problem about turning words into math.

I'm going to assume you know what an integer is, so the first tricky part is "consecutive odd integers." Well, whenever you see a word problem with "consecutive integers," you should think:

x, x+1

Right? If the numbers are 2 and 3, that works, or if they're 1047 and 1048, it still works. So what about consecutive ODD integers? If you're not sure, pick a few numbers at random, and see if you can figure out the pattern. For instance, if the younger sister is 7, the next odd number is 9. If the younger sister is 23, the next odd number is 25.

So if the younger sister is n, what can you write for the older sister's age?

Then the rest of it:

"Product" means multiply

"Is" means equals

"X less than Y" means Y - X

"Times" also means multiply

"Sum" means add

If you want to take a swing now, stop here, otherwise I'll go a little further below:

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the product of their ages is just one less than eight times the sum of their ages.

By now you should have that their ages are n and n+2

So we start turning those words above into math.

"the product of their ages" -- n(n+2)

"is" -- =

"one less than" -- we're going to write " -1" at the end of what follows

"eight times" -- 8 x

"the sum of their ages" -- n + (n+2)

try to write it out. If you're stuck, try below here

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you should have:

n(n+2) = 8(n + (n+2)) - 1

From there, expand, combine like terms, and solve for n!

And let me know if you need more help. You can do it!

Answer 2

If n is the age of the younger sibling, then the age of the older sibling must be n + 2 (consecutive odd integers). Using the given information, we set up the equation:

n(n+2) = 8(n + n + 2) - 1

Rearranging, we have:

n² + 2n = 8(2n + 2) - 1

n² + 2n = 16n + 15

n² - 14n - 15 = 0