3/2(x - 10 ) = 1/2 x + 5
expand by using distributive property
3/2 x - 15 = 1/2 x + 5
subtract (1/2 x ) on both sides
x - 15 = 5
add 15 on both sides
x = 20
answer
C. x = 20
$27 x 18 students = 486 actual cost.
$30 x 10 students = 300 estimated total cost using compatible numbers.
$20 x 20 students = 400 estimated total cost using compatible numbers. (better option because it is nearer to the actual cost)
Compatible numbers are numbers that can easily be multiplied or divided using mental computation.
Compatible number for 27 and 18 can be: 30 and 20 OR 20 and 20 OR 30 and 10 OR 20 and 10.
However, there is a rule in multiplying the compatible numbers, when one number is increased the other number must be decreased.
So 27 can be increased to 30; while 18 can be decreased to 10 to get a product of 300.
27 can be decreased to 20; while 18 can be increased to 20 to get a product of 400.
So first, you have to get two of the same variables to cancel out. Let's do this for x. In order for the x's to cancel out, we could multiply the bottom problem by 2.
(2) 3x-6y=24
After multiplying all the numbers by 2, you get the equation 6x-12y=48
The set of equations is now
-6x+2y=12
6x-12y=48
Now you can add them. The x variables cancel out, so you are left with the y variable.
2y+-12y=-10y and 12+48=60
Then you would divide 60 by -10 to get y=-6.
You would plug the answer for y into one of the original equations, lets do the top one. -6x+2y=12 becomes -6x+2(-6)=12
You'd multiply the 2 and -6 to get -12 so the equation is
-6x-12=12
The negative 12 turn positive and you add to both sides to get the -6x alone.
-6x-12=12
+12=12
-6x=24
Then divide 24 by -6
X=4
(-4,-6) is your final answer.
