Three times the sum of two numbers is greater than 30. The difference in the two numbers is less than or equal to five. Which system of inequalities is represented of the two unknown numbers?
A. 3x + y 30
x - y ≤ 5
B. 3(x + y) 30
x - y ≤ 5
C. 3(x - y) 30
x + y ≤ 5
D. 3x + 3y 30
x - y ≥ 5

Question

Three times the sum of two numbers is greater than 30. The difference in the two numbers is less than or equal to five. Which system of inequalities is represented of the two unknown numbers?
	A.	3x + y > 30 
x - y ≤ 5
	B.	3(x + y) > 30 
x - y ≤ 5
	C.	3(x - y) > 30 
x + y ≤ 5
	D.	3x + 3y > 30 
x - y ≥ 5

anonymous · Answer

$$
\text{Let's break it down.}\
\text{First, we have "three times the sum of two numbers is greater than 30", i.e.}\
\ \ \ 3(x+y)>30\
\text{ where }x,y\text{ are our two numbers.}\
\text{Next, we see "the difference in the two numbers is less than or equal to five", i.e.}\
\ \ \ x-y\le5\
\text{Now... which answer choice is correct?}
$$