Step-by-step explanation:
Assign variables to the integers
Let the larger integer be 'A' and the smaller 'b'
Write Equations based on the Question
Since the sum of the integers is 75, then A + b = 75 (eq
1)
Since the larger number is three times more than the smaller, then A = 3b (eq2)
Combine the Equations and solve for variables
By substituting the value of A in eq1 into eq2
⇒ 3b + b = 75
4b = 75
b = ⁷⁵/₄ = 18.25
By substituting the value of b into eq1
⇒ A = 3(⁷⁵/₄)
A = ²²⁵/₄ = 56.25
Check our Answer:
A + b = 56.25 + 18.75 = 75
39 is the answer
If $x$ is the larger integer, then the smaller integer is $x-3$. We find the sum and set it equal to 75:$x+x-3=75\qquad\Rightarrow \qquad 2x=78\qquad\Rightarrow \qquad x=39$The larger integer is $\boxed{39}$.
