What are 5 mixed numbers that all add up to ten using only (1/3)s and (1/4)s?

I can come close and go over and under but I NEVER hit exactly ten. I'd love if someone can help me please. Thanks!

2 1/4 + 1 3/4 = 4

1/3 + 1 1/3 + 4 1/3 = 6

4+6=10, so just add up the mixed numbers.

Thank you very Steve! I appreciate your time and help.

To find 5 mixed numbers that add up to ten using only (1/3)s and (1/4)s, we can use a method called trial and error. Let's start by setting up some variables:

Let's say we have the following mixed numbers:

a + (1/3)
b + (1/3)
c + (1/3)
d + (1/4)
e + (1/4)

Now, we need to set up equations to find the values of a, b, c, d, and e. Since the question states that the sum should equal ten, we have:

(a + (1/3)) + (b + (1/3)) + (c + (1/3)) + (d + (1/4)) + (e + (1/4)) = 10

To simplify the equation, we can combine like terms:

(a + b + c) + (1/3 + 1/3 + 1/3) + (1/4 + 1/4) + (d + e) = 10

(a + b + c) + (3/3) + (2/4) + (d + e) = 10

(a + b + c) + 1 + 1/2 + (d + e) = 10

(a + b + c + d + e) + 3/2 = 10

Now, let's try different values for the variables a, b, c, d, and e while keeping the equation balanced:

1/3 + 1/3 + 1/3 + 1/4 + 1/4 = 5/6 + 1/4 + 1/4 = 5/6 + 1/2 = 10/6 + 3/6 = 13/6

So, one possible solution is a = 1, b = 1, c = 1, d = 1/4, e = 1/4.

To find more solutions, you can continue trying different combinations of values for a, b, c, d, and e until you find other mixed numbers that add up to ten. Remember to keep the equation balanced at all times.

Please note that there may be more than one solution, and this method may require some trial and error to find them.