To find the GCF, first you must factor the 2 or more numbers. The GCF is the highest factor the numbers have in common. for example: you have 12 and 8. If you factor out the numbers for 12, you get 1,2,3,4,6,12 For 8, you get: 1,2,4,8 the GCF of this pair is 4 because it is the highest number that goes into both 8 and 12. To find the LCM, you must find the first number that was multiplied and it must be the same. lets take 3 and 5. Multiply 3 by as many numbers you can think of. For now, lets just go up to 10. 3, 6, 9, 12 15, 18, 21, 24, 27, 30 now to the same for 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50 in both 3 and 5, the first set of numbers that match in 30- therefore the LCM of 3 and 5 in 30. I hope this helps!
<span><span><span>1. a = b means a is equal to b. 2. a ≠ b means a does not equal b.Operations1. Addition: If a = b then a + c = b + c.</span></span><span><span>2. Subtraction: If <span>a = </span>b then a – c = b– c. 3. Multiplication: If a = b then ac = bc. <span>4. Division: If a = b and <span>c ≠ </span>0 then a/c = b/c.</span></span></span></span>
To solve this problem, you'll need to set up a system of equations.
Assume a = # of adult tickets sold
Assume s = # of student tickets sold
2: a + s = 216; 1: 10.25a+ 8s= 2117.25
2: <<As the total number of tickets sold from both sides is equal to 216>>
1: <<Each adults ticket (a) costs $10.25 and each student ticket (s) costs $8, and the total amount of money earned (2117.25) from sales is the combination of these two))>>
Note that there are two ways to solve systems of equations (by elimnation and substitution), in this case I'll use elimnation as substitution requires one of the variables in one of the two equations to be isolated.
In this case, I'll elimnate a.
a + s = 216
10.25a + 8s = 2117.25
In order to elimnate a, it has to be equal to - 10.25 so that it cancels out + 10.25 (so you have to multiply everything on the first equation by 10.25 ((what you do to one part, you'll do to all the other parts)).
-10.25a -10.25s = -2214
10.25a + 8s = 2117.25
a cancels, and now you solve accordingly.
-2.25s/-2.25 = -96.75/-2.25
s = 43
You could solve for a using this same method, but it's easier to use the first formula <<a+s=216>> to find a.
