four consecutive multiples of 13 add up to 286. what is the largest number?
divide 286 by 13 and get 22
so, you want 4 numbers which add to 22.
2 consecutive numbers which ad to 11 are 5,6
so, the 4 consecutive numbers are 4,5,6,7
Multiply by 13 and add them up to get 286.
Well, let's do some calculations with a twist of humor, shall we?
To find the largest number among four consecutive multiples of 13, we'll divide the sum (286) by 4. Mathematically speaking, dividing 286 by 4 equals 71.5. However, since we're looking for a whole number, it seems we've encountered a bit of a problem. You see, numbers don't like to be split right down the middle!
To overcome this odd number dilemma, we'll have to bring in our investigative skills. We can start by taking the nearest whole number to 71.5, which is 71. But alas! 71 is not a multiple of 13 that will give us consecutive numbers.
So, let's try something else. If we subtract 1 from 71, we get 70 -- also known as a multiple of 10. But, unfortunately, it still isn't a multiple of 13!
With a bit of frustration, we go back to 71. This time, we add 1 to it, giving us 72. Aha! We finally have a winner.
So, the largest number among the four consecutive multiples of 13 that add up to 286 is none other than 72. It's always important to remember that numbers can be funny and sometimes don't follow our expectations!
Let's solve this step-by-step.
To find four consecutive multiples of 13 that add up to 286, we can set up the equation:
13x + 13(x + 1) + 13(x + 2) + 13(x + 3) = 286
Simplifying the equation:
13x + 13x + 13 + 13x + 26 + 13x + 39 = 286
Combine like terms:
52x + 78 = 286
Subtract 78 from both sides:
52x = 286 - 78
Simplify:
52x = 208
Divide both sides by 52:
x = 208 / 52
x = 4
Now, we can find the largest number by substituting the value of x back into the equation:
Largest number = 13(x + 3)
Largest number = 13(4 + 3)
Largest number = 13(7)
Largest number = 91
Therefore, the largest number is 91.
To find the largest number among four consecutive multiples of 13 that add up to 286, we can use algebraic equations.
Let's assume the first number is "x." Then, the four consecutive multiples of 13 would be x, x+13, x+26, and x+39.
The sum of these four numbers is given as 286, so we can write an equation:
x + (x + 13) + (x + 26) + (x + 39) = 286
Simplifying the equation:
4x + 78 = 286
Subtracting 78 from both sides:
4x = 208
Dividing both sides by 4:
x = 52
Therefore, the largest number among the four consecutive multiples of 13 is x + 39, which is 52 + 39 = 91.