There are 16 sixth graders and 20 seventh graders in a club. the club wants to organize members into equal size groups. each group will only have sixth or only seventh graders. how many students will be in each group if each group has the greatest number if club members

Finding the Least Common Multiple, 4, we can easily then divide each group (6th and 7 graders) by 4.
16 6th graders ÷ 4 = 4 groups
20 7th graders ÷ 4 = 5 groups
So, the the 6th graders will have 4 groups each with 4 people (LCM).
The 7th graders will have 5 groups each also with 4 people ( LCM).
Hope this helps!

Sixth graders can have 4 groups of 4
seventh graders can have 5 groups of 4

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12