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

3(x + y) >= 12
3x + 2y <= 15

sub in your answer choices and see which one satisfies both inequalities
A. x = 2, y = -1
3(2 + (-1) >= 12
3(2 - 1) >= 12
3(1) >= 12 (incorrect)...not this one...no need to check the other equation because they have to both work.

B. x = 3 and y = 2
3(3 + 2) >= 12
3(5) >= 12
15 >= 12 (correct)
now check the other one
3x + 2y <= 15
3(3) + 2(2) < = 15
9 + 4 <= 15
13 <= 15 (correct) THIS ONE

C. x = 5 and y = 1
3(5 + 1) >= 12
3(6) >= 12
18 >= 12 (correct)
check other one
3(5) + 2(1) <= 15
15 + 2 <= 15
17 <= 15 (incorrect..not this one

D. x = 4 and y =1
3(4 + 1) >= 12
3(5) >= 12
15 >= 12 (correct)
check the other one
3(4) + 2(1) <= 15
12 + 2 <= 15
14 <= 15 (correct)
This is correct also...

Can there be 2 answers ?

Answer 2

No there is only one! Wow! you did a lot! Thanks soooo much! I have a lot of trouble with these.

Answer 3

I think I see my mistake...I think the first inequality should be :
3x + y >= 12
and then there is 3x + 2y <= 15

D. x = 4 and y = 1
3(4) + 1 >= 12
12 + 1 >= 12
13 >= 12 (correct)
now the other one
3(4) + 2(1) <= 15
12 + 2 <= 15
14 <= 15 (correct)
It is D

Answer 4

Could you help me on another one. Im having problems with this. Ill make a new question.

Answer 5

sure....tag me

Answer 6

ok