What are two mixed numbers so that the sum is 7 2/4 and the difference is 5
a + b = 7 2/4 which is 7.5
a - b = 5
2 a = 12 2/4
a = 6 1/4
b = 7 2/4 - 6 1/4 = 1 1/4
Not helping
Not understanding please what is the answer and how do you work this problem
want the answer
To find two mixed numbers that satisfy the given conditions, we will use algebraic equations. Let's represent the two mixed numbers as follows:
First mixed number: a b/c
Second mixed number: d e/f
According to the given conditions, the sum of the two mixed numbers is 7 2/4, and the difference is 5. We can set up the following equations:
Equation 1: a + d = 7
Equation 2: b/c + e/f = 2/4 (since 2/4 is the same as 1/2)
Now, we need to find a common denominator to combine the fractions in Equation 2. The common denominator for c and f is c * f.
Multiplying Equation 2 by c * f, we get:
b * f + e * c = 2 * c * f / 4
Simplifying the equation by multiplying both sides by 4 and rearranging, we have:
4b * f + 4e * c = 2 * c * f
Next, we need to represent b and e in terms of c and f. We know that b/c is the fractional part of the first mixed number, and e/f is the fractional part of the second mixed number.
So, b = q * c + r (where q is the whole number part of b, and r is the remainder)
and e = s * f + t (where s is the whole number part of e, and t is the remainder)
Substituting b and e into Equation 2, we have:
(q * c + r) * f + (s * f + t) * c = 2 * c * f
Expanding and simplifying the equation, we get:
q * c * f + r * f + s * f * c + t * c = 2 * c * f
Now, we can rearrange the equation to isolate the terms involving f on one side:
q * c * f + s * f * c = 2 * c * f - r * f - t * c
Dividing both sides of the equation by c * f, we have:
q + s * c = 2 - (r * f + t * c) / (c * f)
Now, we have an equation relating the whole number parts (q and s) and the remainders (r and t) with the given conditions.
From the equation a + d = 7, we can see that a and d must be positive integers since the sum is a whole number. We can test different values for a and d to find the corresponding values for q, r, s, and t.
Using the condition that the difference must be 5, we can evaluate the expression |(r * f + t * c) / (c * f)|.
We keep testing different values for a and d until we find a solution where the whole number parts and remainders satisfy all the conditions.