Final answer:
The value of a that makes the equation 'three times the quantity a + 4 equals four times the quantity a - 1' true is 16, found by using the distributive property and isolating the variable.
Step-by-step explanation:
To solve the equation "three times the quantity a + 4 equals four times the quantity a - 1" we first translate it into a mathematical expression:
3(a + 4) = 4(a - 1).
Next, we apply the distributive property:
3a + 12 = 4a - 4.
To find the value of a, we need to isolate the variable on one side of the equation. We can do this by subtracting 3a from both sides:
12 = a - 4.
Adding 4 to both sides gives us the final answer:
a = 16.
Therefore, the value of a that makes the sentence true is 16.