A bag of marbles contains only purple and yellow marbles. The bag has three times as many yellow marbles as purple. The bag contains 164 total marbles. Write an equation or system of equations to determine how many of each color of marble is in the bag. Define your variable(s) and expressions. Show how you checked your answer.

123 purple

Step-by-step explanation:

164/4 = 41

41 = yellow

3 times more purple

41 x 3 = 123

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.