Finding numbers, word equation

Question

Find three consecutive odd integers such that four times the sum of the first and second is 11 more than 3 times the third.

Answer 1

Let's call the 1st odd integer x

Then the next consecutive odd integers are 2 apart: x + 2 and x + 4

4 times the sum of the 1st two will look like 4(x + x + 2)

11 more than 3 times the third is 3(x + 4) + 11

So the equation to solve is 4(2x + 2) = 3(x + 4) + 11 Use the distributive property to eliminate the parentheses.

8x + 8 = 3x + 12 + 11

5x = 15

So x = 3 and the other numbers are 5 and 7

Check: 4(3 + 5) = 3(7) + 11

12 + 20 = 21 + 11; 32 = 32

Answer 2

When interpreting word problems it is important to break down each part of the question:

"Find three consecutive odd integers..."

Let's call the lowest odd integer is "L", the next consecutive odd integer "M", and then next consecutive odd integer after that "N" (I just picked random letters to represent these numbers). Because they are consecutive, we know that:

M = L + 2 (the same way that we know 9 = 7 + 2 or 3 = 1 + 2)

N = M + 2 and N = L + 4 (the same way that we know that 9 = 5 + 4 and 9 = 7 + 2)

This relationship gives us a baseline to work with moving forward with the question.

"...four times the sum of the first and second is 11 more than 3 times the third."

This relationship will give us the equation we want to work with.

"four times the sum of the first and second" is saying: 4(L + M)

"11 more than 3 times the third" is saying: 3(N) + 11

"is" relates these two parts to each other, allowing us to set them equal to each other. Try writing out that relationship based on this information.

You can then use the relationship we described above from our knowledge that these numbers are consecutive to each other to solve for each of the three values.

If you would like any additional help with this or similar math questions, please feel free to reach out to schedule a session. I'd be more than happy to help walk you through similar types of problems!