Please help with this algebra question.?

Question

The larger of two positive integers is five more than twice the smaller integer. The product of the integers is 52. What are the two integers?The smaller integer is___and the larger integer is___. This is a review question and I just can't figure it out without getting decimals, and i'm unsure of the answer. Please help. First right answer gets best answer.

Answer 1

n₂ > n₁
n₂ = 2n₁+5
n₁n₂ = 52
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First find pairs of numbers that multiply to make 52. There are only three such pairs, so it won't take long to test them against the other two criteria.

Answer 2

Always start by making variables for the numbers you're trying to find out.

Let "S" be the smaller number.
Let "L" be the larger number.

Next, translate from English to math.

> "The larger of two positive integers..."

L ...

> "...is..."

L = ...

>"...five more than..."

L = 5 + ...

> "... twice the smaller integer."

L = 5 + 2(S)

That's the end of the sentence, so that's your first equation. Now for the second.

> "The product of the integers..."

(L)(S) ...

> "...is 52."

(L)(S) = 52


You now have these two equations:

L = 5 + 2(S)
(L)(S) = 52

If you know how to solve simultaneous equations, then you should have everything you need.

If you're still stuck, try taking the "5 + 2S" from the first equation, and substitute that for the "S" in the second equation. That will turn the 2nd equation into an equation with just "S" in it. Solve for "S"; then you should be able to substitute again to solve for "L".

Answer 3

x = larger integer, y = smaller
x = 2y + 5 (five more than twice the smaller)

xy = 52 (their product is 52)

Substitute 2y + 5 into the second equation for x
(2y + 5)y = 52
2y^2 + 5y = 52 now get = 0 to solve the quadratic
2y^2 + 5y - 52 = 0
(2y + 13)(y - 4) = 0
y = -13/2 or y = 4 cannot be -13/2

so y = 4, and x = 2y + 5 makes x = 2(4) + 5 = 13

4 and 13

Answer 4

I agree with the above answer of 13 and 4. This is because if you take 4 twice itself...that will give you 8. Add 5 to give you 13...then if you multiply 13 and 4...you will get 52.