Question

The sum of three times a number and a second number will total 12 or greater. The sum of three times the first number and twice the second number is less than or equal to 15. Find the two numbers.
A. first number = 2 and second number = -1
B. first number = 3 and second number = 2
C. first number = 5 and second number = 1
D. first number = 4 and second number = 1

Answer 1

@agent0smith

Answer 2

D

Answer 3

^ not a helpful answer

let the first number be x, second number y

sum of three times a number and a second number will total 12 or greater
\[\Large 3x + y \ge 12\]
sum of three times the first number and twice the second number is less than or equal to 15
\[\Large 3x + 2y \le 15\]

Answer 4

Now we have the two inequalities, you can just plug in the numbers they give to see which works:

A. first number = 2 and second number = -1
B. first number = 3 and second number = 2
C. first number = 5 and second number = 1
D. first number = 4 and second number = 1

remember BOTH inequalities have to be true for the numbers to be a solution
\[\Large 3x + y \ge 12 \]\[\Large 3x + 2y \le 15\]

Answer 5

So after i subtract 3x from both sides of the first equation, then plug the y value into equation 2, then ill have \[3x + 2(-3 + 12) \le 15\]

Answer 6

\[3x -6 + 24 \le 15\]
then ill get
\[3x + 18 \le 15\]
then I subtract 18 from both sides, divide both sides by 3 and \[x \le -1\]

Answer 7

No... you can't solve them that way. Just plug in numbers and check.

Answer 8

No you cant do that as you are dealing with inequalities
So all you have to do is substitute the options and see

Answer 9

A. first number = 2 and second number = -1 ======> x = 2, y = -1
plug them into the inequalities and check if BOTH are true. Do the same for each of A, B, C, D

Answer 10

soo the answer would be C right?

Answer 11

Well show us your work....

C. first number = 5 and second number = 1
so x=5, y=1, plug them in
\[\Large 3*5 + 1 \ge 12\] \[\Large 3*5 + 2*1 \le 15\]

Are they both true?

Answer 12

No.. i just realized that on my notes..

Answer 13

the answers D. because if you plug in the 4 for x and add one its greater than 12 but if you plug 4 in for x on equ. 2 than add 2, 15 is still greater

Answer 14

\[\Large 3*4 + 1 \ge 12\]\[\Large 3*4 + 2*1 \le 15\]

D works :)